diff --git a/ENUME/projectB/Code/task1Newton.m b/ENUME/projectB/Code/task1Newton.m index 472be1cd..a4b69513 100644 --- a/ENUME/projectB/Code/task1Newton.m +++ b/ENUME/projectB/Code/task1Newton.m @@ -1,12 +1,17 @@ interval = [-5, 10]; rootBrackets = rootBracketing(@taskFunction, interval(1), interval(2)); -printGraph(@taskFunction, 'Newton', @newtonMethod, interval, rootBrackets, 'Approximate zeros of function for method of '); - +% printGraph(@taskFunction, 'Newton', @newtonMethod, interval, rootBrackets, 'Approximate zeros of function for method of '); +printGraph(@polynomial, 'Newton', @newtonMethod, interval, rootBrackets, 'Approximate zeros of function for method of '); + function y = taskFunction(x) y = -2.1 + 0.3*x - x*exp(1)^(-x); end +function y = polynomial(x) + y = -2 * x^4 + 12 * x^3 + 4* x^2 + 1 * x + 3; +end + function [zero, iterations] = newtonMethod(taskFunction, a, b, tolerance) [iterations, iteration, zero] = initialize(a, b); [zero, iterations] = newtonLoop(iterations, iteration, zero, a, b, tolerance, taskFunction); diff --git a/ENUME/projectB/Code/task2MM1.m b/ENUME/projectB/Code/task2MM1.m index 997ebff4..1be8f388 100644 --- a/ENUME/projectB/Code/task2MM1.m +++ b/ENUME/projectB/Code/task2MM1.m @@ -3,7 +3,7 @@ rootBrackets = rootBracketing(@polynomial, interval(1), interval(2)); printGraph(@polynomial, 'MM1', @mm1, interval, rootBrackets, 'Approximate zeros of function for method of '); -printComplexGraph(@polynomial, 'MM1', @mm1, [-1 + i, 0], 'Aproximate complex roots of polynomial'); +printComplexGraph(@polynomial, 'MM1', @mm1, [-1 - i, 1 + i], 'Aproximate complex roots of polynomial'); function y = polynomial(x) y = -2 * x^4 + 12 * x^3 + 4* x^2 + 1 * x + 3; diff --git a/ENUME/projectB/Code/task2MM2.m b/ENUME/projectB/Code/task2MM2.m index 1a0b1038..a2f5fea8 100644 --- a/ENUME/projectB/Code/task2MM2.m +++ b/ENUME/projectB/Code/task2MM2.m @@ -3,7 +3,7 @@ rootBrackets = rootBracketing(@polynomial, interval(1), interval(2)); printGraph(@polynomial, 'MM2', @mm2, interval, rootBrackets, 'Approximate zeros of function for method of '); -printComplexGraph(@polynomial, 'MM2', @mm2, [-1 + i, 0], 'Aproximate complex roots of polynomial'); +printComplexGraph(@polynomial, 'MM2', @mm2, [-1 - i, 1 + i], 'Aproximate complex roots of polynomial'); % the polynomial function for task 2 function y = polynomial(x) diff --git a/ENUME/projectB/Code/task3.m b/ENUME/projectB/Code/task3.m index d837642a..bc3dc3e5 100644 --- a/ENUME/projectB/Code/task3.m +++ b/ENUME/projectB/Code/task3.m @@ -3,7 +3,7 @@ rootBrackets = rootBracketing(@polynomial, interval(1), interval(2)); printGraph(@polynomial, 'Laguerre', @laguerre, interval, rootBrackets, 'Approximate zeros of function for method of '); -printComplexGraph(@polynomial, 'Laguerre', @laguerre, [-1 + i, 0], 'Aproximate complex roots of polynomial'); +printComplexGraph(@polynomial, 'Laguerre', @laguerre, [-1 - i, 1 + i], 'Aproximate complex roots of polynomial'); function y = 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"/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc" 1165713224 4850 80dc9bab7f31fb78a000ccfed0e27cab "" "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" @@ -141,37 +141,40 @@ "/usr/share/texmf/web2c/texmf.cnf" 1613593815 38841 799d1dd9682a55ce442e10c99777ecc1 "" "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1635008389 5160710 ecf427ae8fa19139d8691f526e47bb9b "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1635008460 2570450 6e12b1c097cbda0f70015645294afd24 "" - "report.aux" 1638504678 12204 a9d5dac550ff738ea4300ead5ddac656 "pdflatex" - "report.out" 1638504678 2504 fe20c5958a2a6290fbb81d61fae213a3 "pdflatex" - "report.tex" 1638504676 43420 70bcc7876122160d8e2c9a5bcb6cc6b7 "" - "report.toc" 1638504678 7132 0a121cbe34751c9bc1d3f315a0dbe8d7 "pdflatex" + "report.aux" 1638507354 12337 1bac7703aef60a1b6e8cca4333a496f5 "pdflatex" + "report.out" 1638507354 2579 30783b09b42f2c8326374f2da71401ca "pdflatex" + "report.tex" 1638507353 45449 014d4e961e0a6f2dd778097bd3343303 "" + "report.toc" 1638507354 7224 e318ad443102294ddff095b98f2dcb4e "pdflatex" "task1Newtonoverall.eps" 1638502568 42219 4f139cb2eedf6f47c363dda08bab184a "" "task1Newtonzommedleft.eps" 1638502585 17046 67b575c8001c8fbf35bd390dae75f654 "" "task1Newtonzommedright.eps" 1638502602 17986 7cdd5dde9138709561727a5a3a255b3f "" "task1falsepositionoverall.eps" 1638502478 44376 078759826c2f42cdfcbcd0ebe3278712 "" "task1falsepositionzommedleft.eps" 1638502499 20632 4d6074ef6933c98f378ed7aadc29415f "" "task1falsepositionzommedright.eps" 1638502529 17120 9c556abc12f06094869f0d416a04ebdb "" - "task2mm1complexzommeddown.eps" 1638502758 21306 df345847da59b889ea4bfbbaf49cbdc5 "" - "task2mm1complexzommedleft.eps" 1638502733 17087 6efd17077d23716f2ea821563edb545b "" - "task2mm1complexzommedup.eps" 1638502777 20522 c93e4cf62bb478d72e752f22a71212ca "" - "task2mm1overall.eps" 1638502653 42434 0d82fbaed547150f630d2af455da7bba "" - "task2mm1zommedleft.eps" 1638502668 18731 3c827550010982fa488a4272dc1f790f "" - "task2mm1zommedright.eps" 1638502682 16218 bd0fa1b18e395eaa3d0c28ff8e445cb2 "" - "task2mm2complexzommedleft.eps" 1638503397 17333 62290f19560a5ecb66f8984622b3e6b1 "" - "task2mm2complexzommedmiddle.eps" 1638503416 16594 d21577c10cc8d3089f5b1306c13b64ec "" - "task2mm2complexzommedup.eps" 1638503430 17336 e23730b5cdec4242b9fa839e6f74caf9 "" - "task2mm2overall.eps" 1638503331 42230 fa2aef400c94bb5367b4510827e44206 "" - "task2mm2zommedleft.eps" 1638503342 17890 efc34f4c7c03e8178277f867b303a26a "" - "task2mm2zommedright.eps" 1638503357 17932 b05a6814bd81e2e38aca1dd69f78f396 "" - "task3complexdown.eps" 1638502897 16835 2d468ddce7e68fcbe088338d25b32d60 "" - "task3complexoverall.eps" 1638502871 15531 460ce0df8bf19149751e96ddc7bc8ef5 "" - "task3complexup.eps" 1638502909 16935 34fe8b70f5cdedddbbf74b0c67184521 "" - "task3left.eps" 1638502829 16781 ab3eae088b1639d0422ad90dacb32213 "" - "task3overall.eps" 1638502816 42160 af911b057f554cc94854f2b156aca3b3 "" - "task3right.eps" 1638502846 17218 184d626c324afb39ab4c27e6908d7c04 "" + "task2mm1complexdown.eps" 1638506722 17299 1fa77f0a41926706873d83a814bff721 "" + "task2mm1complexmiddle.eps" 1638506735 15057 eac7832e9bcff79b8317ae5f41d1b41e "" + "task2mm1complexoverall.eps" 1638506710 16860 80a854eff892e3b8c92b701a0ecf7c06 "" + "task2mm1complexup.eps" 1638506748 15773 def3746a97e3734c69dc76dcf8d66767 "" + "task2mm1realleft.eps" 1638506679 17067 7d98dee50a12b60ebd9ec5753ec1b796 "" + "task2mm1realoverall.eps" 1638506665 42438 54988f0bcc9d270c96cd340638ac9fe6 "" + "task2mm1realright.eps" 1638506694 17105 4717e7e531eced52280eb0871ba667bb "" + "task2mm2complexleft.eps" 1638506838 17136 b11aea0d8b30724647900254a53e7ebf "" + "task2mm2complexoverall.eps" 1638506804 17747 2fd31ee05bd96d61ed584da833dd05ee "" + "task2mm2complexright.eps" 1638506824 16509 8e385570735d35633adc5cd9d56cb5be "" + "task2mm2complexup.eps" 1638506851 17389 4824b9e0b8ddcc940d9de1f7db78a6c9 "" + "task2mm2realleft.eps" 1638506781 16999 525bce845c0fe56b7b8352616432aa3a "" + "task2mm2realoverall.eps" 1638506769 42234 52dc9450f5d9701df4f0622be28c4b67 "" + "task2mm2realright.eps" 1638506792 17592 1fc47be7b9c871078ea94ffb113a4407 "" + "task3complexleft.eps" 1638507230 16074 ce978148d148b56dad2baeb454788d14 "" + "task3complexoverall.eps" 1638507199 16613 22c3cb5ea4a67991b6a6bcb7052488ce "" + "task3complexright.eps" 1638507217 18005 5eafca9521abca03514af86924a748c1 "" + "task3complexup.eps" 1638507240 17027 81ba37a8266741701c53ef33b14e0e69 "" + "task3left.eps" 1638507170 18391 e0e4e9f4b5be91f62e6639ab0430fcc0 "" + "task3overall.eps" 1638507159 42160 9075b8be2587e6b044f2559bd4bae3b0 "" + "task3right.eps" 1638507181 17899 1844b7b7b64a84e56fe120724b5ce71c "" (generated) - "report.aux" "report.pdf" "report.toc" "report.out" + "report.aux" "report.log" diff --git a/ENUME/projectB/Report/report.fls b/ENUME/projectB/Report/report.fls index 8cd16bae..f1033356 100644 --- a/ENUME/projectB/Report/report.fls +++ b/ENUME/projectB/Report/report.fls @@ -877,138 +877,160 @@ INPUT ./task1Newtonzommedright.eps INPUT ./task1Newtonzommedright-eps-converted-to.pdf INPUT ./task1Newtonzommedright-eps-converted-to.pdf INPUT ./task1Newtonzommedright-eps-converted-to.pdf -INPUT ./task2mm1overall.eps -INPUT ./task2mm1overall.eps -INPUT task2mm1overall.eps -INPUT ./task2mm1overall.eps -INPUT ./task2mm1overall.eps -INPUT ./task2mm1overall-eps-converted-to.pdf -INPUT ./task2mm1overall-eps-converted-to.pdf -INPUT ./task2mm1overall.eps -INPUT ./task2mm1overall-eps-converted-to.pdf -INPUT ./task2mm1overall-eps-converted-to.pdf -INPUT ./task2mm1overall-eps-converted-to.pdf -INPUT ./task2mm1zommedleft.eps -INPUT ./task2mm1zommedleft.eps -INPUT task2mm1zommedleft.eps -INPUT ./task2mm1zommedleft.eps -INPUT ./task2mm1zommedleft.eps -INPUT ./task2mm1zommedleft-eps-converted-to.pdf -INPUT ./task2mm1zommedleft-eps-converted-to.pdf -INPUT ./task2mm1zommedleft.eps -INPUT ./task2mm1zommedleft-eps-converted-to.pdf -INPUT ./task2mm1zommedleft-eps-converted-to.pdf -INPUT ./task2mm1zommedleft-eps-converted-to.pdf -INPUT ./task2mm1zommedright.eps -INPUT ./task2mm1zommedright.eps -INPUT task2mm1zommedright.eps -INPUT ./task2mm1zommedright.eps -INPUT ./task2mm1zommedright.eps -INPUT ./task2mm1zommedright-eps-converted-to.pdf -INPUT ./task2mm1zommedright-eps-converted-to.pdf -INPUT ./task2mm1zommedright.eps -INPUT ./task2mm1zommedright-eps-converted-to.pdf -INPUT ./task2mm1zommedright-eps-converted-to.pdf -INPUT ./task2mm1zommedright-eps-converted-to.pdf -INPUT ./task2mm1complexzommedleft.eps -INPUT ./task2mm1complexzommedleft.eps -INPUT task2mm1complexzommedleft.eps -INPUT ./task2mm1complexzommedleft.eps -INPUT ./task2mm1complexzommedleft.eps -INPUT ./task2mm1complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm1complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm1complexzommedleft.eps -INPUT ./task2mm1complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm1complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm1complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm1complexzommeddown.eps -INPUT ./task2mm1complexzommeddown.eps -INPUT task2mm1complexzommeddown.eps -INPUT ./task2mm1complexzommeddown.eps -INPUT ./task2mm1complexzommeddown.eps -INPUT ./task2mm1complexzommeddown-eps-converted-to.pdf -INPUT ./task2mm1complexzommeddown-eps-converted-to.pdf -INPUT ./task2mm1complexzommeddown.eps -INPUT ./task2mm1complexzommeddown-eps-converted-to.pdf -INPUT ./task2mm1complexzommeddown-eps-converted-to.pdf -INPUT ./task2mm1complexzommeddown-eps-converted-to.pdf -INPUT ./task2mm1complexzommedup.eps -INPUT ./task2mm1complexzommedup.eps -INPUT task2mm1complexzommedup.eps -INPUT ./task2mm1complexzommedup.eps -INPUT ./task2mm1complexzommedup.eps -INPUT ./task2mm1complexzommedup-eps-converted-to.pdf -INPUT ./task2mm1complexzommedup-eps-converted-to.pdf -INPUT ./task2mm1complexzommedup.eps -INPUT ./task2mm1complexzommedup-eps-converted-to.pdf -INPUT ./task2mm1complexzommedup-eps-converted-to.pdf -INPUT ./task2mm1complexzommedup-eps-converted-to.pdf -INPUT ./task2mm2overall.eps -INPUT ./task2mm2overall.eps -INPUT task2mm2overall.eps -INPUT ./task2mm2overall.eps -INPUT ./task2mm2overall.eps -INPUT ./task2mm2overall-eps-converted-to.pdf -INPUT ./task2mm2overall-eps-converted-to.pdf -INPUT ./task2mm2overall.eps -INPUT ./task2mm2overall-eps-converted-to.pdf -INPUT ./task2mm2overall-eps-converted-to.pdf -INPUT ./task2mm2overall-eps-converted-to.pdf -INPUT ./task2mm2zommedleft.eps -INPUT ./task2mm2zommedleft.eps -INPUT task2mm2zommedleft.eps -INPUT ./task2mm2zommedleft.eps -INPUT ./task2mm2zommedleft.eps -INPUT ./task2mm2zommedleft-eps-converted-to.pdf -INPUT ./task2mm2zommedleft-eps-converted-to.pdf -INPUT ./task2mm2zommedleft.eps -INPUT ./task2mm2zommedleft-eps-converted-to.pdf -INPUT ./task2mm2zommedleft-eps-converted-to.pdf -INPUT ./task2mm2zommedleft-eps-converted-to.pdf -INPUT ./task2mm2zommedright.eps -INPUT ./task2mm2zommedright.eps -INPUT task2mm2zommedright.eps -INPUT ./task2mm2zommedright.eps -INPUT ./task2mm2zommedright.eps -INPUT ./task2mm2zommedright-eps-converted-to.pdf -INPUT ./task2mm2zommedright-eps-converted-to.pdf -INPUT ./task2mm2zommedright.eps -INPUT ./task2mm2zommedright-eps-converted-to.pdf -INPUT ./task2mm2zommedright-eps-converted-to.pdf -INPUT ./task2mm2zommedright-eps-converted-to.pdf -INPUT ./task2mm2complexzommedleft.eps -INPUT ./task2mm2complexzommedleft.eps -INPUT task2mm2complexzommedleft.eps -INPUT ./task2mm2complexzommedleft.eps -INPUT ./task2mm2complexzommedleft.eps -INPUT ./task2mm2complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm2complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm2complexzommedleft.eps -INPUT ./task2mm2complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm2complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm2complexzommedleft-eps-converted-to.pdf -INPUT ./task2mm2complexzommedmiddle.eps -INPUT ./task2mm2complexzommedmiddle.eps -INPUT task2mm2complexzommedmiddle.eps -INPUT ./task2mm2complexzommedmiddle.eps -INPUT ./task2mm2complexzommedmiddle.eps -INPUT ./task2mm2complexzommedmiddle-eps-converted-to.pdf -INPUT ./task2mm2complexzommedmiddle-eps-converted-to.pdf -INPUT ./task2mm2complexzommedmiddle.eps -INPUT ./task2mm2complexzommedmiddle-eps-converted-to.pdf -INPUT ./task2mm2complexzommedmiddle-eps-converted-to.pdf -INPUT ./task2mm2complexzommedmiddle-eps-converted-to.pdf -INPUT ./task2mm2complexzommedup.eps -INPUT ./task2mm2complexzommedup.eps -INPUT task2mm2complexzommedup.eps -INPUT ./task2mm2complexzommedup.eps -INPUT ./task2mm2complexzommedup.eps -INPUT ./task2mm2complexzommedup-eps-converted-to.pdf -INPUT ./task2mm2complexzommedup-eps-converted-to.pdf -INPUT ./task2mm2complexzommedup.eps -INPUT ./task2mm2complexzommedup-eps-converted-to.pdf -INPUT ./task2mm2complexzommedup-eps-converted-to.pdf -INPUT ./task2mm2complexzommedup-eps-converted-to.pdf +INPUT ./task2mm1realoverall.eps +INPUT ./task2mm1realoverall.eps +INPUT task2mm1realoverall.eps +INPUT ./task2mm1realoverall.eps +INPUT ./task2mm1realoverall.eps +INPUT ./task2mm1realoverall-eps-converted-to.pdf +INPUT ./task2mm1realoverall-eps-converted-to.pdf +INPUT ./task2mm1realoverall.eps +INPUT ./task2mm1realoverall-eps-converted-to.pdf +INPUT ./task2mm1realoverall-eps-converted-to.pdf +INPUT ./task2mm1realoverall-eps-converted-to.pdf +INPUT ./task2mm1realleft.eps +INPUT ./task2mm1realleft.eps +INPUT task2mm1realleft.eps +INPUT ./task2mm1realleft.eps +INPUT ./task2mm1realleft.eps +INPUT ./task2mm1realleft-eps-converted-to.pdf +INPUT ./task2mm1realleft-eps-converted-to.pdf +INPUT ./task2mm1realleft.eps +INPUT ./task2mm1realleft-eps-converted-to.pdf +INPUT ./task2mm1realleft-eps-converted-to.pdf +INPUT ./task2mm1realleft-eps-converted-to.pdf +INPUT ./task2mm1realright.eps +INPUT ./task2mm1realright.eps +INPUT task2mm1realright.eps +INPUT ./task2mm1realright.eps +INPUT ./task2mm1realright.eps +INPUT ./task2mm1realright-eps-converted-to.pdf +INPUT ./task2mm1realright-eps-converted-to.pdf +INPUT ./task2mm1realright.eps +INPUT ./task2mm1realright-eps-converted-to.pdf +INPUT ./task2mm1realright-eps-converted-to.pdf +INPUT ./task2mm1realright-eps-converted-to.pdf +INPUT ./task2mm1complexoverall.eps +INPUT ./task2mm1complexoverall.eps +INPUT task2mm1complexoverall.eps +INPUT ./task2mm1complexoverall.eps +INPUT ./task2mm1complexoverall.eps +INPUT ./task2mm1complexoverall-eps-converted-to.pdf +INPUT ./task2mm1complexoverall-eps-converted-to.pdf +INPUT ./task2mm1complexoverall.eps +INPUT ./task2mm1complexoverall-eps-converted-to.pdf +INPUT ./task2mm1complexoverall-eps-converted-to.pdf +INPUT ./task2mm1complexoverall-eps-converted-to.pdf +INPUT ./task2mm1complexdown.eps +INPUT ./task2mm1complexdown.eps +INPUT task2mm1complexdown.eps +INPUT ./task2mm1complexdown.eps +INPUT ./task2mm1complexdown.eps +INPUT ./task2mm1complexdown-eps-converted-to.pdf +INPUT ./task2mm1complexdown-eps-converted-to.pdf +INPUT ./task2mm1complexdown.eps +INPUT ./task2mm1complexdown-eps-converted-to.pdf +INPUT ./task2mm1complexdown-eps-converted-to.pdf +INPUT ./task2mm1complexdown-eps-converted-to.pdf +INPUT ./task2mm1complexmiddle.eps +INPUT ./task2mm1complexmiddle.eps +INPUT task2mm1complexmiddle.eps +INPUT ./task2mm1complexmiddle.eps +INPUT ./task2mm1complexmiddle.eps +INPUT ./task2mm1complexmiddle-eps-converted-to.pdf +INPUT ./task2mm1complexmiddle-eps-converted-to.pdf +INPUT ./task2mm1complexmiddle.eps +INPUT ./task2mm1complexmiddle-eps-converted-to.pdf +INPUT ./task2mm1complexmiddle-eps-converted-to.pdf +INPUT ./task2mm1complexmiddle-eps-converted-to.pdf +INPUT ./task2mm1complexup.eps +INPUT ./task2mm1complexup.eps +INPUT task2mm1complexup.eps +INPUT ./task2mm1complexup.eps +INPUT ./task2mm1complexup.eps +INPUT ./task2mm1complexup-eps-converted-to.pdf +INPUT ./task2mm1complexup-eps-converted-to.pdf +INPUT ./task2mm1complexup.eps +INPUT ./task2mm1complexup-eps-converted-to.pdf +INPUT ./task2mm1complexup-eps-converted-to.pdf +INPUT ./task2mm1complexup-eps-converted-to.pdf +INPUT ./task2mm2realoverall.eps +INPUT ./task2mm2realoverall.eps +INPUT task2mm2realoverall.eps +INPUT ./task2mm2realoverall.eps +INPUT ./task2mm2realoverall.eps +INPUT ./task2mm2realoverall-eps-converted-to.pdf +INPUT ./task2mm2realoverall-eps-converted-to.pdf +INPUT ./task2mm2realoverall.eps +INPUT ./task2mm2realoverall-eps-converted-to.pdf +INPUT ./task2mm2realoverall-eps-converted-to.pdf +INPUT ./task2mm2realoverall-eps-converted-to.pdf +INPUT ./task2mm2realleft.eps +INPUT ./task2mm2realleft.eps +INPUT task2mm2realleft.eps +INPUT ./task2mm2realleft.eps +INPUT ./task2mm2realleft.eps +INPUT ./task2mm2realleft-eps-converted-to.pdf +INPUT ./task2mm2realleft-eps-converted-to.pdf +INPUT ./task2mm2realleft.eps +INPUT ./task2mm2realleft-eps-converted-to.pdf +INPUT ./task2mm2realleft-eps-converted-to.pdf +INPUT ./task2mm2realleft-eps-converted-to.pdf +INPUT ./task2mm2realright.eps +INPUT ./task2mm2realright.eps +INPUT task2mm2realright.eps +INPUT ./task2mm2realright.eps +INPUT ./task2mm2realright.eps +INPUT ./task2mm2realright-eps-converted-to.pdf +INPUT ./task2mm2realright-eps-converted-to.pdf +INPUT ./task2mm2realright.eps +INPUT ./task2mm2realright-eps-converted-to.pdf +INPUT ./task2mm2realright-eps-converted-to.pdf +INPUT ./task2mm2realright-eps-converted-to.pdf +INPUT ./task2mm2complexoverall.eps +INPUT ./task2mm2complexoverall.eps +INPUT task2mm2complexoverall.eps +INPUT ./task2mm2complexoverall.eps +INPUT ./task2mm2complexoverall.eps +INPUT ./task2mm2complexoverall-eps-converted-to.pdf +INPUT ./task2mm2complexoverall-eps-converted-to.pdf +INPUT ./task2mm2complexoverall.eps +INPUT ./task2mm2complexoverall-eps-converted-to.pdf +INPUT ./task2mm2complexoverall-eps-converted-to.pdf +INPUT ./task2mm2complexoverall-eps-converted-to.pdf +INPUT ./task2mm2complexright.eps +INPUT ./task2mm2complexright.eps +INPUT task2mm2complexright.eps +INPUT ./task2mm2complexright.eps +INPUT ./task2mm2complexright.eps +INPUT ./task2mm2complexright-eps-converted-to.pdf +INPUT ./task2mm2complexright-eps-converted-to.pdf +INPUT ./task2mm2complexright.eps +INPUT ./task2mm2complexright-eps-converted-to.pdf +INPUT ./task2mm2complexright-eps-converted-to.pdf +INPUT ./task2mm2complexright-eps-converted-to.pdf +INPUT ./task2mm2complexleft.eps +INPUT ./task2mm2complexleft.eps +INPUT task2mm2complexleft.eps +INPUT ./task2mm2complexleft.eps +INPUT ./task2mm2complexleft.eps +INPUT ./task2mm2complexleft-eps-converted-to.pdf +INPUT ./task2mm2complexleft-eps-converted-to.pdf +INPUT ./task2mm2complexleft.eps +INPUT ./task2mm2complexleft-eps-converted-to.pdf +INPUT ./task2mm2complexleft-eps-converted-to.pdf +INPUT ./task2mm2complexleft-eps-converted-to.pdf +INPUT ./task2mm2complexup.eps +INPUT ./task2mm2complexup.eps +INPUT task2mm2complexup.eps +INPUT ./task2mm2complexup.eps +INPUT ./task2mm2complexup.eps +INPUT ./task2mm2complexup-eps-converted-to.pdf +INPUT ./task2mm2complexup-eps-converted-to.pdf +INPUT ./task2mm2complexup.eps +INPUT ./task2mm2complexup-eps-converted-to.pdf +INPUT ./task2mm2complexup-eps-converted-to.pdf +INPUT ./task2mm2complexup-eps-converted-to.pdf INPUT ./task3overall.eps INPUT ./task3overall.eps INPUT task3overall.eps @@ -1053,17 +1075,28 @@ INPUT ./task3complexoverall.eps INPUT ./task3complexoverall-eps-converted-to.pdf INPUT ./task3complexoverall-eps-converted-to.pdf INPUT ./task3complexoverall-eps-converted-to.pdf -INPUT ./task3complexdown.eps -INPUT ./task3complexdown.eps -INPUT task3complexdown.eps -INPUT ./task3complexdown.eps -INPUT ./task3complexdown.eps -INPUT ./task3complexdown-eps-converted-to.pdf -INPUT ./task3complexdown-eps-converted-to.pdf -INPUT ./task3complexdown.eps -INPUT ./task3complexdown-eps-converted-to.pdf -INPUT ./task3complexdown-eps-converted-to.pdf -INPUT ./task3complexdown-eps-converted-to.pdf +INPUT ./task3complexleft.eps +INPUT ./task3complexleft.eps +INPUT task3complexleft.eps +INPUT ./task3complexleft.eps +INPUT ./task3complexleft.eps +INPUT ./task3complexleft-eps-converted-to.pdf +INPUT ./task3complexleft-eps-converted-to.pdf +INPUT ./task3complexleft.eps +INPUT ./task3complexleft-eps-converted-to.pdf +INPUT ./task3complexleft-eps-converted-to.pdf +INPUT ./task3complexleft-eps-converted-to.pdf +INPUT ./task3complexright.eps +INPUT ./task3complexright.eps +INPUT task3complexright.eps +INPUT ./task3complexright.eps +INPUT ./task3complexright.eps +INPUT ./task3complexright-eps-converted-to.pdf +INPUT ./task3complexright-eps-converted-to.pdf +INPUT ./task3complexright.eps +INPUT ./task3complexright-eps-converted-to.pdf +INPUT ./task3complexright-eps-converted-to.pdf +INPUT ./task3complexright-eps-converted-to.pdf INPUT ./task3complexup.eps INPUT ./task3complexup.eps INPUT task3complexup.eps diff --git a/ENUME/projectB/Report/report.log b/ENUME/projectB/Report/report.log index 7d0f29cd..3a2c296e 100644 --- a/ENUME/projectB/Report/report.log +++ b/ENUME/projectB/Report/report.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.10.23) 3 DEC 2021 05:11 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.10.23) 3 DEC 2021 05:55 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -470,7 +470,7 @@ File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] (./report.tocpdfTeX warning (ext4): destination with the same identifier (name{page.1}) has been already used, duplicate ignored \relax -l.28 ...between MM1 and MM2}{24}{subsection.3.3.1} +l.28 ...\numberline {3.3}Results}{24}{section.3.3} % [1 ]) @@ -486,12 +486,12 @@ Package epstopdf Info: Source file: (epstopdf) date: 2021-12-03 04:34:38 (epstopdf) size: 44376 bytes (epstopdf) Output file: -(epstopdf) 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Package epstopdf Info: Output file is already uptodate. - + File: task3complexup-eps-converted-to.pdf Graphic file (type pdf) -Package pdftex.def Info: task3complexup-eps-converted-to.pdf used on input line 580. +Package pdftex.def Info: task3complexup-eps-converted-to.pdf used on input line 619. (pdftex.def) Requested size: 346.29291pt x 178.16519pt. - [23 <./task3right-eps-converted-to.pdf> <./task3complexoverall-eps-converted-to.pdf> <./task3complexdown-eps-converted-to.pdf>] [24 <./task3complexup-eps-converted-to.pdf>] + [26 <./task3complexright-eps-converted-to.pdf> <./task3complexup-eps-converted-to.pdf>] [27] Chapter 4. -LaTeX Font Info: Trying to load font information for T1+fvm on input line 649. +LaTeX Font Info: Trying to load font information for T1+fvm on input line 695. 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PDF statistics: - 1375 PDF objects out of 1440 (max. 8388607) - 1192 compressed objects within 12 object streams - 615 named destinations out of 1000 (max. 500000) - 417 words of extra memory for PDF output out of 10000 (max. 10000000) + 1423 PDF objects out of 1440 (max. 8388607) + 1226 compressed objects within 13 object streams + 622 named destinations out of 1000 (max. 500000) + 440 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/ENUME/projectB/Report/report.out b/ENUME/projectB/Report/report.out index 3e0ccc62..9e93b785 100644 --- a/ENUME/projectB/Report/report.out +++ b/ENUME/projectB/Report/report.out @@ -7,31 +7,32 @@ \BOOKMARK [2][-]{subsection.1.2.1}{Problem}{section.1.2}% 7 \BOOKMARK [2][-]{subsection.1.2.2}{Theoretical Introduction}{section.1.2}% 8 \BOOKMARK [2][-]{subsection.1.2.3}{Results}{section.1.2}% 9 -\BOOKMARK [0][-]{chapter.2}{Find real and complex roots of the polynomial}{}% 10 -\BOOKMARK [1][-]{section.2.1}{Problem}{chapter.2}% 11 -\BOOKMARK [1][-]{section.2.2}{Theoretical Introduction}{chapter.2}% 12 -\BOOKMARK [2][-]{subsection.2.2.1}{MM1}{section.2.2}% 13 -\BOOKMARK [2][-]{subsection.2.2.2}{MM2}{section.2.2}% 14 -\BOOKMARK [1][-]{section.2.3}{Results}{chapter.2}% 15 -\BOOKMARK [2][-]{subsection.2.3.1}{Graphs for MM1}{section.2.3}% 16 -\BOOKMARK [2][-]{subsection.2.3.2}{Graphs for MM2}{section.2.3}% 17 -\BOOKMARK [2][-]{subsection.2.3.3}{Tables for MM1}{section.2.3}% 18 -\BOOKMARK [2][-]{subsection.2.3.4}{Tables for MM2}{section.2.3}% 19 -\BOOKMARK [2][-]{subsection.2.3.5}{Comparison of results between MM1 and MM2}{section.2.3}% 20 -\BOOKMARK [2][-]{subsection.2.3.6}{Comparison of results between Newton's method and MM2}{section.2.3}% 21 -\BOOKMARK [0][-]{chapter.3}{Find real and complex roots of the polynomial using Laguerre's method}{}% 22 -\BOOKMARK [1][-]{section.3.1}{Problem}{chapter.3}% 23 -\BOOKMARK [1][-]{section.3.2}{Theoretical Introduction}{chapter.3}% 24 -\BOOKMARK [1][-]{section.3.3}{Results}{chapter.3}% 25 -\BOOKMARK [2][-]{subsection.3.3.1}{Comparison of results between MM1 and MM2}{section.3.3}% 26 -\BOOKMARK [0][-]{chapter.4}{Code appendix}{}% 27 -\BOOKMARK [1][-]{section.4.1}{Task 1}{chapter.4}% 28 -\BOOKMARK [2][-]{subsection.4.1.1}{task1Bisection.m}{section.4.1}% 29 -\BOOKMARK [2][-]{subsection.4.1.2}{task1Newton.m}{section.4.1}% 30 -\BOOKMARK [1][-]{section.4.2}{Task 2}{chapter.4}% 31 -\BOOKMARK [2][-]{subsection.4.2.1}{task2MM1.m}{section.4.2}% 32 -\BOOKMARK [2][-]{subsection.4.2.2}{task2MM2.m}{section.4.2}% 33 -\BOOKMARK [1][-]{section.4.3}{Task 3}{chapter.4}% 34 -\BOOKMARK [2][-]{subsection.4.3.1}{rootBrackering.m}{section.4.3}% 35 -\BOOKMARK [2][-]{subsection.4.3.2}{printGraph.m}{section.4.3}% 36 -\BOOKMARK [2][-]{subsection.4.3.3}{printComplexGraph.m}{section.4.3}% 37 +\BOOKMARK [2][-]{subsection.1.2.4}{Discussion of results}{section.1.2}% 10 +\BOOKMARK [0][-]{chapter.2}{Find real and complex roots of the polynomial}{}% 11 +\BOOKMARK [1][-]{section.2.1}{Problem}{chapter.2}% 12 +\BOOKMARK [1][-]{section.2.2}{Theoretical Introduction}{chapter.2}% 13 +\BOOKMARK [2][-]{subsection.2.2.1}{MM1}{section.2.2}% 14 +\BOOKMARK [2][-]{subsection.2.2.2}{MM2}{section.2.2}% 15 +\BOOKMARK [1][-]{section.2.3}{Results}{chapter.2}% 16 +\BOOKMARK [2][-]{subsection.2.3.1}{Graphs for MM1}{section.2.3}% 17 +\BOOKMARK [2][-]{subsection.2.3.2}{Graphs for MM2}{section.2.3}% 18 +\BOOKMARK [2][-]{subsection.2.3.3}{Tables for MM1}{section.2.3}% 19 +\BOOKMARK [2][-]{subsection.2.3.4}{Tables for MM2}{section.2.3}% 20 +\BOOKMARK [2][-]{subsection.2.3.5}{Comparison of results between MM1 and MM2}{section.2.3}% 21 +\BOOKMARK [2][-]{subsection.2.3.6}{Comparison of results between Newton's method and MM2}{section.2.3}% 22 +\BOOKMARK [0][-]{chapter.3}{Find real and complex roots of the polynomial using Laguerre's method}{}% 23 +\BOOKMARK [1][-]{section.3.1}{Problem}{chapter.3}% 24 +\BOOKMARK [1][-]{section.3.2}{Theoretical Introduction}{chapter.3}% 25 +\BOOKMARK [1][-]{section.3.3}{Results}{chapter.3}% 26 +\BOOKMARK [2][-]{subsection.3.3.1}{Comparison of results between MM1 and MM2}{section.3.3}% 27 +\BOOKMARK [0][-]{chapter.4}{Code appendix}{}% 28 +\BOOKMARK [1][-]{section.4.1}{Task 1}{chapter.4}% 29 +\BOOKMARK [2][-]{subsection.4.1.1}{task1Bisection.m}{section.4.1}% 30 +\BOOKMARK [2][-]{subsection.4.1.2}{task1Newton.m}{section.4.1}% 31 +\BOOKMARK [1][-]{section.4.2}{Task 2}{chapter.4}% 32 +\BOOKMARK [2][-]{subsection.4.2.1}{task2MM1.m}{section.4.2}% 33 +\BOOKMARK [2][-]{subsection.4.2.2}{task2MM2.m}{section.4.2}% 34 +\BOOKMARK [1][-]{section.4.3}{Task 3}{chapter.4}% 35 +\BOOKMARK [2][-]{subsection.4.3.1}{rootBrackering.m}{section.4.3}% 36 +\BOOKMARK [2][-]{subsection.4.3.2}{printGraph.m}{section.4.3}% 37 +\BOOKMARK [2][-]{subsection.4.3.3}{printComplexGraph.m}{section.4.3}% 38 diff --git a/ENUME/projectB/Report/report.pdf b/ENUME/projectB/Report/report.pdf index f186152e..8a0529db 100644 Binary files a/ENUME/projectB/Report/report.pdf and b/ENUME/projectB/Report/report.pdf differ diff --git a/ENUME/projectB/Report/report.synctex.gz b/ENUME/projectB/Report/report.synctex.gz index 06dadc2e..82f7def1 100644 Binary files a/ENUME/projectB/Report/report.synctex.gz and b/ENUME/projectB/Report/report.synctex.gz differ diff --git a/ENUME/projectB/Report/report.tex b/ENUME/projectB/Report/report.tex index a8509aa5..49e50865 100644 --- a/ENUME/projectB/Report/report.tex +++ b/ENUME/projectB/Report/report.tex @@ -274,6 +274,19 @@ Iteration & root & f(root) \\ \end{tabular} \end{center} +\subsection{Discussion of results} +As we can see and as we could expect from theory Newton method reigns supreme. +It is: +\begin{enumerate} +\item Faster. +Especially for finding first root. It took 36 iterations for false position method to find first root with accuary up to $10^{-10}$ and it took only 6 iterations for the Newton method. +\item More accurate +Not only that we also got more accurate results with Newton method! With first root being so close to the real answer that the matlab calculated the value of this function at this point as exactly equal to 0. For second root the accuary is $10^{6}$ better than for the false position method. +\item Smaller gaps +Looking at graphs we got from both method we can clearly see that the gaps between the final result and each and every step are much smaller for Newton method. This again proves that it is faster and more accurate compared to false position method. +\end{enumerate} + + \chapter{Find real and complex roots of the polynomial} @@ -357,52 +370,60 @@ This method is locally convergent with order of convergence equal to 1.84. It is \subsection{Graphs for MM1} \begin{center} - \includegraphics[scale=0.25]{task2mm1overall.eps} + \includegraphics[scale=0.25]{task2mm1realoverall.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm1zommedleft.eps} + \includegraphics[scale=0.25]{task2mm1realleft.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm1zommedright.eps} + \includegraphics[scale=0.25]{task2mm1realright.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm1complexzommedleft.eps} + \includegraphics[scale=0.25]{task2mm1complexoverall.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm1complexzommeddown.eps} + \includegraphics[scale=0.25]{task2mm1complexdown.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm1complexzommedup.eps} + \includegraphics[scale=0.25]{task2mm1complexmiddle.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm1complexup.eps} \end{center} \subsection{Graphs for MM2} \begin{center} - \includegraphics[scale=0.25]{task2mm2overall.eps} + \includegraphics[scale=0.25]{task2mm2realoverall.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm2zommedleft.eps} + \includegraphics[scale=0.25]{task2mm2realleft.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm2zommedright.eps} + \includegraphics[scale=0.25]{task2mm2realright.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm2complexzommedleft.eps} + \includegraphics[scale=0.25]{task2mm2complexoverall.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm2complexzommedmiddle.eps} + \includegraphics[scale=0.25]{task2mm2complexright.eps} \end{center} \begin{center} - \includegraphics[scale=0.25]{task2mm2complexzommedup.eps} + \includegraphics[scale=0.25]{task2mm2complexleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2complexup.eps} \end{center} \subsection{Tables for MM1} @@ -411,21 +432,22 @@ This method is locally convergent with order of convergence equal to 1.84. It is \hline Iteration & root & f(root) \\ \hline -1 & -1.25 & -20.32 \\ +1 & -1.25 & -20.32 \\ \hline -2 & -1.0009 & -8.0351 \\ +2 & -1.0009 & -8.0351 \\ \hline -3 & -0.76855 & -1.5512 \\ +3 & -0.76855 & -1.5512 \\ \hline -4 & -0.63496 & 0.58064 \\ +4 & -0.63496 & 0.58064 \\ \hline -5 & -0.67945 & -0.023155 \\ +5 & -0.67945 & -0.023155 \\ \hline -6 & -0.67788 & -0.00010725 \\ +6 & -0.67788 & -0.00010725 \\ \hline -7 & -0.67787 & -8.6306e-09 \\ +7 & -0.67787 & -8.6306e-09 \\ +\hline +8 & -0.67787 & 0 \\ \hline -8 & -0.67787 & 0 \\ \hline \end{tabular} @@ -440,11 +462,13 @@ Iteration & root & f(root) \\ \hline 2 & 6.3257 & 4.4966 \\ \hline -3 & 6.3341 & 0.033379 \\ +3 & 6.3341 & 0.033379 \\ \hline -4 & 6.3341 & -1.6916e-06 \\ +4 & 6.3341 & -1.6916e-06 \\ \hline -5 & 6.3341 & -7.1942e-14 \\ +5 & 6.3341 & -7.1942e-14 \\ +\hline + \hline \end{tabular} @@ -455,21 +479,24 @@ Iteration & root & f(root) \\ \hline Iteration & root & f(root) \\ \hline -1 & -0.5-0.5i & 6.1847 \\ +1 & 0+0i & 3 \\ \hline -2 & -0.42823-0.15033i & 2.6872 \\ +2 & -0.0072549-0.12193i & 2.9384 \\ \hline -3 & -0.59202+0.094367i & 1.6012 \\ +3 & 0.069406-0.45062i & 1.7235 \\ \hline -4 & -0.71249-0.0089336i & 0.55524 \\ +4 & 0.19733-0.61224i & 0.82578 \\ \hline -5 & -0.67654+0.00084164i & 0.022962 \\ +5 & 0.16937-0.56334i & 0.047116 \\ \hline -6 & -0.67787+8.4773e-06i & 0.00012412 \\ +6 & 0.17186-0.56551i & 0.0003142 \\ \hline -7 & -0.67787+3.6458e-10i & 8.3668e-09 \\ +7 & 0.17188-0.56551i & 4.4741e-08 \\ +\hline +8 & 0.17188-0.56551i & 2.6645e-15 \\ +\hline +9 & 0.17188-0.56551i & 0 \\ \hline -8 & -0.67787+9.1168e-18i & 1.3321e-16 \\ \hline \end{tabular} @@ -481,15 +508,16 @@ Iteration & root & f(root) \\ \hline Iteration & root & f(root) \\ \hline - 1 & -1.25+0i & -20.32+0i \\ - \hline - 2 & -0.72604-0.25326i & 1.0515-4.0744i \\ - \hline - 3 & -0.68613-0.01483i & -0.11667-0.22303i \\ - \hline - 4 & -0.67788+2.5407e-06i & -0.00010163+3.7123e-05i\\ - \hline - 5 & -0.67787-8.0819e-13i & 1.4105e-11-1.1809e-11i \\ +1 & -1.25+0i & -20.32+0i \\ +\hline +2 & -0.72604-0.25326i & 1.0515-4.0744i \\ +\hline +3 & -0.68613-0.01483i & -0.11667-0.22303i \\ +\hline +4 & -0.67788+2.5407e-06i & -0.00010163+3.7123e-05i \\ +\hline +5 & -0.67787-8.0819e-13i & 1.4105e-11-1.1809e-11i \\ +\hline \hline \end{tabular} @@ -500,15 +528,16 @@ Iteration & root & f(root) \\ \hline Iteration & root & f(root) \\ \hline -1 & 6.25 & 43.43 \\ +1 & 6.25 & 43.43 \\ \hline -2 & 6.3376 & -1.8647 \\ +2 & 6.3376 & -1.8647 \\ \hline -3 & 6.3341 & 0.0029695 \\ +3 & 6.3341 & 0.0029695 \\ \hline -4 & 6.3341 & 1.6294e-08 \\ +4 & 6.3341 & 1.6294e-08 \\ +\hline +5 & 6.3341 & -4.6896e-13 \\ \hline -5 & 6.3341 & -4.6896e-13 \\ \hline \end{tabular} @@ -519,21 +548,27 @@ Iteration & root & f(root) \\ \hline Iteration & root & f(root) \\ \hline -1 & -0.5-0.5i & 6.1847 \\ +1 & 0+0i & 3 \\ \hline -2 & -0.60346-0.076584i & 1.3673 \\ +2 & -0.125+0.85696i & 8.0341 \\ \hline -3 & -0.67709+0.001186i & 0.020767 \\ +3 & 0.16892+0.62593i & 0.94053 \\ \hline -4 & -0.67787+1.518e-08i & 2.2673e-07 \\ +4 & 0.17203+0.56536i & 0.0031354 \\ +\hline +5 & 0.17188+0.56551i & 3.8615e-09 \\ +\hline +6 & 0.17188+0.56551i & 0 \\ \hline -5 & -0.67787-2.0556e-17i & 3.0035e-16 \\ \hline \end{tabular} \end{center} \subsection{Comparison of results between MM1 and MM2} +As we can see MM2 method is much better, it took on average 5 iterations for it to find a root with sufficient accuracy compared to around 7 iterations that MM1 needed to find roots. But MM1 is slightly more accurate. There was also fatal error for one of the complex roots for MM1 where the algorithm failed to calculate the complex part. MM2 correctly calculated complex root while MM1 calculated only real part of the result. + +We can also observe that on graphs with MM2 approaching the root faster than MM1 and MM1 being slightly more accurate. \subsection{Comparison of results between Newton's method and MM2} \chapter{Find real and complex roots of the polynomial using Laguerre's method} @@ -573,7 +608,11 @@ This formula is similar to the one from MM2 but also takes order of the polynomi \end{center} \begin{center} - \includegraphics[scale=0.25]{task3complexdown.eps} + \includegraphics[scale=0.25]{task3complexleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task3complexright.eps} \end{center} \begin{center} @@ -587,11 +626,12 @@ Iteration & root & f(root) \\ \hline 1 & -1.25 & -20.32 \\ \hline -2 & -0.67905 & -0.017268 \\ +2 & -0.67905 & -0.017268 \\ \hline 3 & -0.67787 & -3.1489e-07 \\ \hline -4 & -0.67787 & 0 \\ +4 & -0.67787 & 0 \\ +\hline \hline \hline @@ -603,16 +643,18 @@ Iteration & root & f(root) \\ \hline Iteration & root & f(root) \\ \hline -1 & -1.25 & -20.32 \\ +1 & 6.25 & 43.43 \\ \hline -2 & -0.67905 & -0.017268 \\ +2 & 6.3376 & -1.8647 \\ \hline -3 & -0.67787 & -3.1489e-07 \\ +3 & 6.3341 & 0.0029631 \\ \hline -4 & -0.67787 & 0 \\ +4 & 6.3341 & 7.9942e-09\\ \hline +5 & 6.3341 & -7.1942e-14\\ \hline + \end{tabular} \end{center} @@ -622,15 +664,19 @@ Iteration & root & f(root) \\ \hline Iteration & root & f(root) \\ \hline -1 & -1.25 & -20.32 \\ +1 & 0+0i & 3 \\ \hline -2 & -0.67905 & -0.017268 \\ +2 & -0.042857+0.71586i & 4.1826 \\ \hline -3 & -0.67787 & -3.1489e-07 \\ +3 & 0.172+0.56266i & 0.040584 \\ \hline -4 & -0.67787 & 0 \\ +4 & 0.17188+0.56551i & 2.8484e-06 \\ \hline +5 & 0.17188+0.56551i & 2.2952e-14 \\ \hline +6 & 0.17188+0.56551i & 0 \\ +\hline + \end{tabular} \end{center} @@ -882,7 +928,7 @@ rootBrackets = rootBracketing(@polynomial, interval(1), interval(2)); printGraph(@polynomial, 'MM1', @mm1, interval, rootBrackets, 'Approximate zeros of function for method of '); -printComplexGraph(@polynomial, 'MM1', @mm1, [-1 + i, 0], 'Aproximate complex roots of polynomial'); +printComplexGraph(@polynomial, 'MM1', @mm1, [-1 - i, 1 + i], 'Aproximate complex roots of polynomial'); \end{lstlisting} \end{simplechar} @@ -1083,7 +1129,7 @@ rootBrackets = rootBracketing(@polynomial, interval(1), interval(2)); printGraph(@polynomial, 'MM2', @mm2, interval, rootBrackets, 'Approximate zeros of function for method of '); -printComplexGraph(@polynomial, 'MM2', @mm2, [-1 + i, 0], 'Aproximate complex roots of polynomial'); +printComplexGraph(@polynomial, 'MM2', @mm2, [-1 - i, 1 + i], 'Aproximate complex roots of polynomial'); \end{lstlisting} \end{simplechar} @@ -1210,7 +1256,7 @@ rootBrackets = rootBracketing(@polynomial, interval(1), interval(2)); printGraph(@polynomial, 'Laguerre', @laguerre, interval, rootBrackets, 'Approximate zeros of function for method of '); -printComplexGraph(@polynomial, 'Laguerre', @laguerre, [-1 + i, 0], 'Aproximate complex roots of polynomial'); +printComplexGraph(@polynomial, 'Laguerre', @laguerre, [-1 - i, 1 + i], 'Aproximate complex roots of polynomial'); \end{lstlisting} \end{simplechar} diff --git a/ENUME/projectB/Report/report.toc b/ENUME/projectB/Report/report.toc index 985858f3..57c7bb64 100644 --- a/ENUME/projectB/Report/report.toc +++ b/ENUME/projectB/Report/report.toc @@ -9,91 +9,92 @@ \contentsline {subsection}{\numberline {1.2.1}Problem}{8}{subsection.1.2.1}% \contentsline {subsection}{\numberline {1.2.2}Theoretical Introduction}{8}{subsection.1.2.2}% \contentsline {subsection}{\numberline {1.2.3}Results}{9}{subsection.1.2.3}% -\contentsline {chapter}{\numberline {2}Find real and complex roots of the polynomial}{11}{chapter.2}% -\contentsline {section}{\numberline {2.1}Problem}{11}{section.2.1}% -\contentsline {section}{\numberline {2.2}Theoretical Introduction}{11}{section.2.2}% -\contentsline {subsection}{\numberline {2.2.1}MM1}{12}{subsection.2.2.1}% -\contentsline {subsection}{\numberline {2.2.2}MM2}{13}{subsection.2.2.2}% -\contentsline {section}{\numberline {2.3}Results}{14}{section.2.3}% -\contentsline {subsection}{\numberline {2.3.1}Graphs for MM1}{14}{subsection.2.3.1}% -\contentsline {subsection}{\numberline {2.3.2}Graphs for MM2}{16}{subsection.2.3.2}% -\contentsline {subsection}{\numberline {2.3.3}Tables for MM1}{18}{subsection.2.3.3}% -\contentsline {subsection}{\numberline {2.3.4}Tables for MM2}{19}{subsection.2.3.4}% -\contentsline {subsection}{\numberline {2.3.5}Comparison of results between MM1 and MM2}{20}{subsection.2.3.5}% -\contentsline {subsection}{\numberline {2.3.6}Comparison of results between Newton's method and MM2}{20}{subsection.2.3.6}% -\contentsline {chapter}{\numberline {3}Find real and complex roots of the polynomial using Laguerre's method}{21}{chapter.3}% -\contentsline {section}{\numberline {3.1}Problem}{21}{section.3.1}% -\contentsline {section}{\numberline {3.2}Theoretical Introduction}{21}{section.3.2}% -\contentsline {section}{\numberline {3.3}Results}{22}{section.3.3}% -\contentsline {subsection}{\numberline {3.3.1}Comparison of results between MM1 and MM2}{24}{subsection.3.3.1}% -\contentsline {chapter}{\numberline {4}Code appendix}{25}{chapter.4}% -\contentsline {section}{\numberline {4.1}Task 1}{25}{section.4.1}% -\contentsline {subsection}{\numberline {4.1.1}task1Bisection.m}{25}{subsection.4.1.1}% -\contentsline {subsubsection}{Top of task1Bisection.m}{25}{section*.4}% -\contentsline {subsubsection}{taskFunction}{25}{section*.5}% -\contentsline {subsubsection}{falsePosition}{26}{section*.6}% -\contentsline {subsubsection}{initialize}{26}{section*.7}% -\contentsline {subsubsection}{taskFunction}{26}{section*.8}% -\contentsline {subsubsection}{firstTwoIterations}{27}{section*.9}% -\contentsline {subsubsection}{falsePositionLoop}{27}{section*.10}% -\contentsline {subsubsection}{insideLoop}{28}{section*.11}% -\contentsline {subsubsection}{changeLastTwoAB}{28}{section*.12}% -\contentsline {subsubsection}{calculateZero}{29}{section*.13}% -\contentsline {subsubsection}{newSubInterval}{29}{section*.14}% -\contentsline {subsection}{\numberline {4.1.2}task1Newton.m}{29}{subsection.4.1.2}% -\contentsline {subsubsection}{Top of task1Newton.m}{29}{section*.15}% -\contentsline {subsubsection}{taskFunction}{30}{section*.16}% -\contentsline {subsubsection}{newtonMethod}{30}{section*.17}% -\contentsline {subsubsection}{initialize}{30}{section*.18}% -\contentsline {subsubsection}{newtonLoop}{30}{section*.19}% -\contentsline {subsubsection}{insideLoop}{31}{section*.20}% -\contentsline {subsubsection}{calculateZeroIterations}{31}{section*.21}% -\contentsline {subsubsection}{checkForDivergence}{31}{section*.22}% -\contentsline {section}{\numberline {4.2}Task 2}{32}{section.4.2}% -\contentsline {subsection}{\numberline {4.2.1}task2MM1.m}{32}{subsection.4.2.1}% -\contentsline {subsubsection}{Top of task2MM1}{32}{section*.23}% -\contentsline {subsubsection}{polynomial}{32}{section*.24}% -\contentsline {subsubsection}{mm1}{32}{section*.25}% -\contentsline {subsubsection}{initialize}{33}{section*.26}% -\contentsline {subsubsection}{mm1Loop}{33}{section*.27}% -\contentsline {subsubsection}{insideLoop}{33}{section*.28}% -\contentsline {subsubsection}{createEquationSystem}{34}{section*.29}% -\contentsline {subsubsection}{rootsOfQuadraticFormula}{34}{section*.30}% -\contentsline {subsubsection}{updateApproximations}{34}{section*.31}% -\contentsline {subsubsection}{initializeEquationSystem}{35}{section*.32}% -\contentsline {subsubsection}{solveEquationSystem}{35}{section*.33}% -\contentsline {subsubsection}{createApproximatedQuadraticFormula}{36}{section*.34}% -\contentsline {subsubsection}{findRootsOfQuadraticFormula}{36}{section*.35}% -\contentsline {subsubsection}{chooseNewRoot}{36}{section*.36}% -\contentsline {subsubsection}{addZeroToIterationVector}{36}{section*.37}% -\contentsline {subsubsection}{getWorstApproximationIndex}{37}{section*.38}% -\contentsline {subsubsection}{deleteWorstApproximation}{37}{section*.39}% -\contentsline {subsection}{\numberline {4.2.2}task2MM2.m}{38}{subsection.4.2.2}% -\contentsline {subsubsection}{top of task2MM2.m}{38}{section*.40}% -\contentsline {subsubsection}{polynomial}{38}{section*.41}% -\contentsline {subsubsection}{mm2}{38}{section*.42}% -\contentsline {subsubsection}{initialize}{38}{section*.43}% -\contentsline {subsubsection}{mm2Loop}{39}{section*.44}% -\contentsline {subsubsection}{insideLoop}{39}{section*.45}% -\contentsline {subsubsection}{getABC}{39}{section*.46}% -\contentsline {subsubsection}{findRoots}{39}{section*.47}% -\contentsline {subsubsection}{chooseNewApproximation}{40}{section*.48}% -\contentsline {subsubsection}{updateApproximations}{40}{section*.49}% -\contentsline {subsubsection}{derivative}{40}{section*.50}% -\contentsline {section}{\numberline {4.3}Task 3}{41}{section.4.3}% -\contentsline {subsubsection}{Top of Task 3}{41}{section*.51}% -\contentsline {subsubsection}{polynomial}{41}{section*.52}% -\contentsline {subsubsection}{laguerre}{41}{section*.53}% -\contentsline {subsubsection}{initialize}{42}{section*.54}% -\contentsline {subsubsection}{laguerreLoop}{42}{section*.55}% -\contentsline {subsubsection}{insideLoop}{42}{section*.56}% -\contentsline {subsubsection}{calculateDerrivatives}{43}{section*.57}% -\contentsline {subsubsection}{calculateZ}{43}{section*.58}% -\contentsline {subsubsection}{chooseNewZero}{43}{section*.59}% -\contentsline {subsubsection}{updateZeros}{44}{section*.60}% -\contentsline {subsection}{\numberline {4.3.1}rootBrackering.m}{44}{subsection.4.3.1}% -\contentsline {subsubsection}{updateZeros}{44}{section*.61}% -\contentsline {subsubsection}{initializeValues}{45}{section*.62}% -\contentsline {subsubsection}{bracketingLoop}{46}{section*.63}% -\contentsline {subsection}{\numberline {4.3.2}printGraph.m}{47}{subsection.4.3.2}% -\contentsline {subsection}{\numberline {4.3.3}printComplexGraph.m}{49}{subsection.4.3.3}% +\contentsline {subsection}{\numberline {1.2.4}Discussion of results}{10}{subsection.1.2.4}% +\contentsline {chapter}{\numberline {2}Find real and complex roots of the polynomial}{12}{chapter.2}% +\contentsline {section}{\numberline {2.1}Problem}{12}{section.2.1}% +\contentsline {section}{\numberline {2.2}Theoretical Introduction}{12}{section.2.2}% +\contentsline {subsection}{\numberline {2.2.1}MM1}{13}{subsection.2.2.1}% +\contentsline {subsection}{\numberline {2.2.2}MM2}{14}{subsection.2.2.2}% +\contentsline {section}{\numberline {2.3}Results}{15}{section.2.3}% +\contentsline {subsection}{\numberline {2.3.1}Graphs for MM1}{15}{subsection.2.3.1}% +\contentsline {subsection}{\numberline {2.3.2}Graphs for MM2}{18}{subsection.2.3.2}% +\contentsline {subsection}{\numberline {2.3.3}Tables for MM1}{20}{subsection.2.3.3}% +\contentsline {subsection}{\numberline {2.3.4}Tables for MM2}{21}{subsection.2.3.4}% +\contentsline {subsection}{\numberline {2.3.5}Comparison of results between MM1 and MM2}{22}{subsection.2.3.5}% +\contentsline {subsection}{\numberline {2.3.6}Comparison of results between Newton's method and MM2}{22}{subsection.2.3.6}% +\contentsline {chapter}{\numberline {3}Find real and complex roots of the polynomial using Laguerre's method}{23}{chapter.3}% +\contentsline {section}{\numberline {3.1}Problem}{23}{section.3.1}% +\contentsline {section}{\numberline {3.2}Theoretical Introduction}{23}{section.3.2}% +\contentsline {section}{\numberline {3.3}Results}{24}{section.3.3}% +\contentsline {subsection}{\numberline {3.3.1}Comparison of results between MM1 and MM2}{27}{subsection.3.3.1}% +\contentsline {chapter}{\numberline {4}Code appendix}{28}{chapter.4}% +\contentsline {section}{\numberline {4.1}Task 1}{28}{section.4.1}% +\contentsline {subsection}{\numberline {4.1.1}task1Bisection.m}{28}{subsection.4.1.1}% +\contentsline {subsubsection}{Top of task1Bisection.m}{28}{section*.4}% +\contentsline {subsubsection}{taskFunction}{28}{section*.5}% +\contentsline {subsubsection}{falsePosition}{29}{section*.6}% +\contentsline {subsubsection}{initialize}{29}{section*.7}% +\contentsline {subsubsection}{taskFunction}{29}{section*.8}% +\contentsline {subsubsection}{firstTwoIterations}{30}{section*.9}% +\contentsline {subsubsection}{falsePositionLoop}{30}{section*.10}% +\contentsline {subsubsection}{insideLoop}{31}{section*.11}% +\contentsline {subsubsection}{changeLastTwoAB}{31}{section*.12}% +\contentsline {subsubsection}{calculateZero}{32}{section*.13}% +\contentsline {subsubsection}{newSubInterval}{32}{section*.14}% +\contentsline {subsection}{\numberline {4.1.2}task1Newton.m}{32}{subsection.4.1.2}% +\contentsline {subsubsection}{Top of task1Newton.m}{32}{section*.15}% +\contentsline {subsubsection}{taskFunction}{33}{section*.16}% +\contentsline {subsubsection}{newtonMethod}{33}{section*.17}% +\contentsline {subsubsection}{initialize}{33}{section*.18}% +\contentsline {subsubsection}{newtonLoop}{33}{section*.19}% +\contentsline {subsubsection}{insideLoop}{34}{section*.20}% +\contentsline {subsubsection}{calculateZeroIterations}{34}{section*.21}% +\contentsline {subsubsection}{checkForDivergence}{34}{section*.22}% +\contentsline {section}{\numberline {4.2}Task 2}{35}{section.4.2}% +\contentsline {subsection}{\numberline {4.2.1}task2MM1.m}{35}{subsection.4.2.1}% +\contentsline {subsubsection}{Top of task2MM1}{35}{section*.23}% +\contentsline {subsubsection}{polynomial}{35}{section*.24}% +\contentsline {subsubsection}{mm1}{35}{section*.25}% +\contentsline {subsubsection}{initialize}{36}{section*.26}% +\contentsline {subsubsection}{mm1Loop}{36}{section*.27}% +\contentsline {subsubsection}{insideLoop}{36}{section*.28}% +\contentsline {subsubsection}{createEquationSystem}{37}{section*.29}% +\contentsline {subsubsection}{rootsOfQuadraticFormula}{37}{section*.30}% +\contentsline {subsubsection}{updateApproximations}{37}{section*.31}% +\contentsline {subsubsection}{initializeEquationSystem}{38}{section*.32}% +\contentsline {subsubsection}{solveEquationSystem}{38}{section*.33}% +\contentsline {subsubsection}{createApproximatedQuadraticFormula}{39}{section*.34}% +\contentsline {subsubsection}{findRootsOfQuadraticFormula}{39}{section*.35}% +\contentsline {subsubsection}{chooseNewRoot}{39}{section*.36}% +\contentsline {subsubsection}{addZeroToIterationVector}{39}{section*.37}% +\contentsline {subsubsection}{getWorstApproximationIndex}{40}{section*.38}% +\contentsline {subsubsection}{deleteWorstApproximation}{40}{section*.39}% +\contentsline {subsection}{\numberline {4.2.2}task2MM2.m}{41}{subsection.4.2.2}% +\contentsline {subsubsection}{top of task2MM2.m}{41}{section*.40}% +\contentsline {subsubsection}{polynomial}{41}{section*.41}% +\contentsline {subsubsection}{mm2}{41}{section*.42}% +\contentsline {subsubsection}{initialize}{41}{section*.43}% +\contentsline {subsubsection}{mm2Loop}{42}{section*.44}% +\contentsline {subsubsection}{insideLoop}{42}{section*.45}% +\contentsline {subsubsection}{getABC}{42}{section*.46}% +\contentsline {subsubsection}{findRoots}{42}{section*.47}% +\contentsline {subsubsection}{chooseNewApproximation}{43}{section*.48}% +\contentsline {subsubsection}{updateApproximations}{43}{section*.49}% +\contentsline {subsubsection}{derivative}{43}{section*.50}% +\contentsline {section}{\numberline {4.3}Task 3}{44}{section.4.3}% +\contentsline {subsubsection}{Top of Task 3}{44}{section*.51}% +\contentsline {subsubsection}{polynomial}{44}{section*.52}% +\contentsline {subsubsection}{laguerre}{44}{section*.53}% +\contentsline {subsubsection}{initialize}{45}{section*.54}% +\contentsline {subsubsection}{laguerreLoop}{45}{section*.55}% +\contentsline {subsubsection}{insideLoop}{45}{section*.56}% +\contentsline {subsubsection}{calculateDerrivatives}{46}{section*.57}% +\contentsline {subsubsection}{calculateZ}{46}{section*.58}% +\contentsline {subsubsection}{chooseNewZero}{46}{section*.59}% +\contentsline {subsubsection}{updateZeros}{47}{section*.60}% +\contentsline {subsection}{\numberline {4.3.1}rootBrackering.m}{47}{subsection.4.3.1}% +\contentsline {subsubsection}{updateZeros}{47}{section*.61}% +\contentsline {subsubsection}{initializeValues}{48}{section*.62}% +\contentsline {subsubsection}{bracketingLoop}{49}{section*.63}% +\contentsline {subsection}{\numberline {4.3.2}printGraph.m}{50}{subsection.4.3.2}% +\contentsline {subsection}{\numberline {4.3.3}printComplexGraph.m}{52}{subsection.4.3.3}% diff --git a/ENUME/projectB/Report/task1Newtonoverall-eps-converted-to.pdf b/ENUME/projectB/Report/task1Newtonoverall-eps-converted-to.pdf index 84963556..b3c14d5f 100644 Binary files a/ENUME/projectB/Report/task1Newtonoverall-eps-converted-to.pdf and b/ENUME/projectB/Report/task1Newtonoverall-eps-converted-to.pdf differ diff --git a/ENUME/projectB/Report/task1Newtonzommedleft-eps-converted-to.pdf 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GS @@ -667,7 +720,7 @@ GS GR GR GS -[0.72 0 0 0.72 344.22173 468.38455] CT +[0.72 0 0 0.72 384.66031 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -678,7 +731,7 @@ GS GR GR GS -[0.72 0 0 0.72 458.35528 468.38455] CT +[0.72 0 0 0.72 480.65885 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -689,7 +742,7 @@ GS GR GR GS -[0.72 0 0 0.72 572.49427 468.38455] CT +[0.72 0 0 0.72 576.662 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -700,7 +753,7 @@ GS GR GR GS -[0.72 0 0 0.72 686.62781 468.38455] CT +[0.72 0 0 0.72 672.66054 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -711,7 +764,7 @@ GS GR GR GS -[0.72 0 0 0.72 800.76675 468.38455] CT +[0.72 0 0 0.72 768.66364 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -722,7 +775,7 @@ GS GR GR GS -[0.72 0 0 0.72 914.90029 468.38455] CT +[0.72 0 0 0.72 864.66227 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -733,7 +786,7 @@ GS GR GR GS -[0.72 0 0 0.72 1029.03927 468.38455] CT +[0.72 0 0 0.72 960.66537 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -744,7 +797,7 @@ GS GR GR GS -[0.72 0 0 0.72 1143.17281 468.38455] CT +[0.72 0 0 0.72 1056.66391 364.2386] CT 0.149 GC /Helvetica 13.889 F GS @@ -755,6 +808,17 @@ GS GR GR GS +[0.72 0 0 0.72 1152.66702 364.2386] CT +0.149 GC +/Helvetica 13.889 F +GS +[1 0 0 1 0 0] CT +-15.5 13 moveto +1 -1 scale +(6.34) t +GR +GR +GS [0.72 0 0 0.72 0 0.08002] CT 0.149 GC 2 setlinecap @@ -772,8 +836,8 @@ GS 1 LJ 0.694 LW N -248.997 874.034 M -263.85 874.034 L +248.997 855.384 M +263.849 855.384 L S GR GS @@ -783,8 +847,8 @@ GS 1 LJ 0.694 LW N -248.997 759.451 M -263.85 759.451 L +248.997 736.996 M +263.849 736.996 L S GR GS @@ -794,8 +858,8 @@ GS 1 LJ 0.694 LW N -248.997 644.867 M -263.85 644.867 L +248.997 618.608 M +263.849 618.608 L S GR GS @@ -805,8 +869,8 @@ GS 1 LJ 0.694 LW N -248.997 530.284 M -263.85 530.284 L +248.997 500.22 M +263.849 500.22 L S GR GS @@ -816,8 +880,8 @@ GS 1 LJ 0.694 LW N -248.997 415.701 M -263.85 415.701 L +248.997 381.832 M +263.849 381.832 L S GR GS @@ -827,8 +891,8 @@ GS 1 LJ 0.694 LW N -248.997 301.118 M -263.85 301.118 L +248.997 263.444 M +263.849 263.444 L S GR GS @@ -838,12 +902,34 @@ GS 1 LJ 0.694 LW N -248.997 186.534 M -263.85 186.534 L +248.997 145.056 M +263.849 145.056 L S GR GS -[0.72 0 0 0.72 175.27731 629.38448] CT +[0.72 0 0 0.72 175.27716 615.95673] CT +0.149 GC +/Helvetica 13.889 F +GS +[1 0 0 1 0 0] CT +-23 4.5 moveto +1 -1 scale +(-60) t +GR +GR +GS +[0.72 0 0 0.72 175.27716 530.71737] CT +0.149 GC +/Helvetica 13.889 F +GS +[1 0 0 1 0 0] CT +-23 4.5 moveto +1 -1 scale +(-40) t +GR +GR +GS +[0.72 0 0 0.72 175.27716 445.47797] CT 0.149 GC /Helvetica 13.889 F GS @@ -854,18 +940,7 @@ GS GR GR GS -[0.72 0 0 0.72 175.27731 546.88454] CT -0.149 GC -/Helvetica 13.889 F -GS -[1 0 0 1 0 0] CT --23 4.5 moveto -1 -1 scale -(-10) t -GR -GR -GS -[0.72 0 0 0.72 175.27731 464.38456] CT +[0.72 0 0 0.72 175.27716 360.23861] CT 0.149 GC /Helvetica 13.889 F GS @@ -876,18 +951,7 @@ GS GR GR GS -[0.72 0 0 0.72 175.27731 381.88457] CT -0.149 GC -/Helvetica 13.889 F -GS -[1 0 0 1 0 0] CT --18 4.5 moveto -1 -1 scale -(10) t -GR -GR -GS -[0.72 0 0 0.72 175.27731 299.38461] CT +[0.72 0 0 0.72 175.27716 274.99923] CT 0.149 GC /Helvetica 13.889 F GS @@ -898,18 +962,7 @@ GS GR GR GS -[0.72 0 0 0.72 175.27731 216.88463] CT -0.149 GC -/Helvetica 13.889 F -GS -[1 0 0 1 0 0] CT --18 4.5 moveto -1 -1 scale -(30) t -GR -GR -GS -[0.72 0 0 0.72 175.27731 134.38467] CT +[0.72 0 0 0.72 175.27716 189.75987] CT 0.149 GC /Helvetica 13.889 F GS @@ -920,7 +973,18 @@ GS GR GR GS -[0.72 0 0 0.72 713.87812 51.37999] CT +[0.72 0 0 0.72 175.27716 104.52049] CT +0.149 GC +/Helvetica 13.889 F +GS +[1 0 0 1 0 0] CT +-18 4.5 moveto +1 -1 scale +(60) t +GR +GR +GS +[0.72 0 0 0.72 713.87799 51.38001] CT /Helvetica-Bold 15.278 F GS [1 0 0 1 0 0] CT @@ -935,21 +999,23 @@ GS 1 LJ 0.694 LW N -248.819 122.004 M -319.559 147.236 L -478.086 204.33 L -636.605 261.976 L -795.131 320.177 L -953.65 378.935 L -1112.176 438.253 L -1270.695 498.134 L -1429.221 558.58 L -1587.74 619.593 L -1734.175 676.48 L +248.82 209.862 M +267.575 213.931 L +400.913 243.143 L +534.25 272.638 L +667.582 302.418 L +800.919 332.484 L +934.251 362.839 L +1067.588 393.483 L +1200.92 424.417 L +1334.257 455.644 L +1467.589 487.164 L +1600.926 518.978 L +1734.174 551.069 L S GR GS -[0.72 0 0 0.72 230.08274 106.08975] CT +[0.72 0 0 0.72 288.65716 175.14264] CT 1 0 0 RC N 0 -3.819 M @@ -969,7 +1035,7 @@ cp f GR GS -[0.72 0 0 0.72 230.08274 106.08975] CT +[0.72 0 0 0.72 288.65716 175.14264] CT /Helvetica 13.889 F GS [1 0 0 1 0 0] CT @@ -979,7 +1045,7 @@ GS GR GR GS -[0.72 0 0 0.72 1229.71317 479.7681] CT +[0.72 0 0 0.72 1129.45361 368.18579] CT 0 1 0 RC N /f235133452{0 -3.819 M @@ -1000,21 +1066,21 @@ f235133452 f GR GS -[0.72 0 0 0.72 1190.08127 464.36012] CT +[0.72 0 0 0.72 1096.11898 360.22597] CT 0 1 0 RC N f235133452 f GR GS -[0.72 0 0 0.72 1190.14112 464.38456] CT +[0.72 0 0 0.72 1096.16934 360.23861] CT 0 1 0 RC N f235133452 f GR GS -[0.72 0 0 0.72 1190.14112 464.38456] CT +[0.72 0 0 0.72 1096.16934 360.23861] CT 0 1 0 RC N f235133452