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/usr/share/texlive/texmf-dist/tex/latex/bera/t1fvm.fd diff --git a/ENUME/projectB/Report/report.log b/ENUME/projectB/Report/report.log index 5af7a7d7..4fee78a6 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 04:31 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.10.23) 3 DEC 2021 04:53 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.39 ...4.1.2}task1Newton.m}{16}{subsection.4.1.2} +l.39 ...4.1.2}task1Newton.m}{25}{subsection.4.1.2} 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Chapter 3. -[10 +[17 -] [11] +] +Package epstopdf Info: Source file: +(epstopdf) date: 2021-12-03 04:40:16 +(epstopdf) size: 42160 bytes +(epstopdf) Output file: +(epstopdf) date: 2021-12-03 04:51:55 +(epstopdf) size: 20523 bytes +(epstopdf) Command: +(epstopdf) \includegraphics on input line 288. +Package epstopdf Info: Output file is already uptodate. + +File: task3overall-eps-converted-to.pdf Graphic file (type pdf) + +Package pdftex.def Info: task3overall-eps-converted-to.pdf used on input line 288. +(pdftex.def) Requested size: 346.29291pt x 178.16519pt. +Package epstopdf Info: Source file: +(epstopdf) date: 2021-12-03 04:40:29 +(epstopdf) size: 16781 bytes +(epstopdf) Output file: +(epstopdf) date: 2021-12-03 04:53:16 +(epstopdf) size: 9493 bytes +(epstopdf) Command: +(epstopdf) \includegraphics on input line 293. +Package epstopdf Info: Output file is already uptodate. + +File: task3left-eps-converted-to.pdf Graphic file (type pdf) + +Package pdftex.def Info: 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z%yr>$5%Wuk5-1g#IB$%wEEJvUcPQ``m;3tAK1x5qoljAV$W!d#MGn}Nr+i{)q$x(- zX~< z?_az;TwfH1{u?QLS#=G0`6l*sbCWqe7yj&NC xTu-RI9QlU+%@X^U7Mz2Md{KEQ_H?rGvPBm9G9va2%;`DwG0JJu;DQC}{{b!}iM#*+ diff --git a/ENUME/projectB/Report/report.tex b/ENUME/projectB/Report/report.tex index 9d14326c..3e0fa79d 100644 --- a/ENUME/projectB/Report/report.tex +++ b/ENUME/projectB/Report/report.tex @@ -85,6 +85,18 @@ This is called \emph{modified regula falsi} or \emph{Illinois algorithm}. It is superlinearly convergent, globally convergent and length of intervals we get in each iterations converges to zero. \subsection{Results} +\begin{center} + \includegraphics[scale=0.25]{task1falsepositionoverall.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task1falsepositionzommedleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task1falsepositionzommedright.eps} +\end{center} + \section{b) the Newton's method} @@ -108,6 +120,19 @@ This method as opposed to \emph{regula falsi} method is locally convergent, shou Newton's method is also effective if the function derrivative is far from zero, so the slope of the function is steep, conversely if the derrivative is close to zero the method is not recommended. \subsection{Results} +\begin{center} + \includegraphics[scale=0.25]{task1Newtonoverall.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task1Newtonzommedleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task1Newtonzommedright.eps} +\end{center} + + \chapter{Find real and complex roots of the polynomial} @@ -189,6 +214,54 @@ This method is locally convergent with order of convergence equal to 1.84. It is \section{Results} +\begin{center} + \includegraphics[scale=0.25]{task2mm1overall.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm1zommedleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm1zommedright.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm1complexzommedleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm1complexzommeddown.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm1complexzommedup.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2overall.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2zommedleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2zommedright.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2complexzommedleft.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2complexzommedmiddle.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task2mm2complexzommedup.eps} +\end{center} + \subsection{Comparison of results between MM1 and MM2} \subsection{Comparison of results between Newton's method and MM2} @@ -210,6 +283,33 @@ $n$ - order of the polynomial This formula is similar to the one from MM2 but also takes order of the polynomial into consideration. In general this method is better. For polynomials with real roots it is globally convergent. It does not have formal analysis for complex roots but it usually shows good numerical properties, although divergence may happen. \section{Results} + +\begin{center} + \includegraphics[scale=0.25]{task3overall.eps} +\end{center} + + +\begin{center} + \includegraphics[scale=0.25]{task3left.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task3right.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task3complexoverall.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task3complexdown.eps} +\end{center} + +\begin{center} + \includegraphics[scale=0.25]{task3complexup.eps} +\end{center} + + \subsection{Comparison of results between MM1 and MM2} \chapter{Code appendix} diff --git a/ENUME/projectB/Report/report.toc b/ENUME/projectB/Report/report.toc index 3b5183b8..901445d8 100644 --- a/ENUME/projectB/Report/report.toc +++ b/ENUME/projectB/Report/report.toc @@ -5,91 +5,91 @@ \contentsline {subsubsection}{Properties of \emph {false position method}}{4}{section*.2}% \contentsline {paragraph}{Improvement to the method}{4}{section*.3}% \contentsline {subsection}{\numberline {1.1.3}Results}{5}{subsection.1.1.3}% -\contentsline {section}{\numberline {1.2}b) the Newton's method}{5}{section.1.2}% -\contentsline {subsection}{\numberline {1.2.1}Problem}{5}{subsection.1.2.1}% -\contentsline {subsection}{\numberline {1.2.2}Theoretical Introduction}{5}{subsection.1.2.2}% -\contentsline {subsection}{\numberline {1.2.3}Results}{5}{subsection.1.2.3}% -\contentsline {chapter}{\numberline {2}Find real and complex roots of the polynomial}{6}{chapter.2}% -\contentsline {section}{\numberline {2.1}Problem}{6}{section.2.1}% -\contentsline {section}{\numberline {2.2}Theoretical Introduction}{6}{section.2.2}% -\contentsline {subsection}{\numberline {2.2.1}MM1}{7}{subsection.2.2.1}% -\contentsline {subsection}{\numberline {2.2.2}MM2}{8}{subsection.2.2.2}% -\contentsline {section}{\numberline {2.3}Results}{9}{section.2.3}% -\contentsline {subsection}{\numberline {2.3.1}Comparison of results between MM1 and MM2}{9}{subsection.2.3.1}% -\contentsline {subsection}{\numberline {2.3.2}Comparison of results between Newton's method and MM2}{9}{subsection.2.3.2}% -\contentsline {chapter}{\numberline {3}Find real and complex roots of the polynomial using Laguerre's method}{10}{chapter.3}% -\contentsline {section}{\numberline {3.1}Problem}{10}{section.3.1}% -\contentsline {section}{\numberline {3.2}Theoretical Introduction}{10}{section.3.2}% -\contentsline {section}{\numberline {3.3}Results}{11}{section.3.3}% -\contentsline {subsection}{\numberline {3.3.1}Comparison of results between MM1 and MM2}{11}{subsection.3.3.1}% -\contentsline {chapter}{\numberline {4}Code appendix}{12}{chapter.4}% -\contentsline {section}{\numberline {4.1}Task 1}{12}{section.4.1}% -\contentsline {subsection}{\numberline {4.1.1}task1Bisection.m}{12}{subsection.4.1.1}% -\contentsline {subsubsection}{Top of task1Bisection.m}{12}{section*.4}% -\contentsline {subsubsection}{taskFunction}{12}{section*.5}% -\contentsline {subsubsection}{falsePosition}{13}{section*.6}% -\contentsline {subsubsection}{initialize}{13}{section*.7}% -\contentsline {subsubsection}{taskFunction}{13}{section*.8}% -\contentsline {subsubsection}{firstTwoIterations}{14}{section*.9}% -\contentsline {subsubsection}{falsePositionLoop}{14}{section*.10}% -\contentsline {subsubsection}{insideLoop}{15}{section*.11}% -\contentsline {subsubsection}{changeLastTwoAB}{15}{section*.12}% -\contentsline {subsubsection}{calculateZero}{16}{section*.13}% -\contentsline {subsubsection}{newSubInterval}{16}{section*.14}% -\contentsline {subsection}{\numberline {4.1.2}task1Newton.m}{16}{subsection.4.1.2}% -\contentsline {subsubsection}{Top of task1Newton.m}{16}{section*.15}% -\contentsline {subsubsection}{taskFunction}{17}{section*.16}% -\contentsline {subsubsection}{newtonMethod}{17}{section*.17}% -\contentsline {subsubsection}{initialize}{17}{section*.18}% -\contentsline {subsubsection}{newtonLoop}{17}{section*.19}% -\contentsline {subsubsection}{insideLoop}{18}{section*.20}% -\contentsline {subsubsection}{calculateZeroIterations}{18}{section*.21}% -\contentsline {subsubsection}{checkForDivergence}{18}{section*.22}% -\contentsline {section}{\numberline {4.2}Task 2}{19}{section.4.2}% -\contentsline {subsection}{\numberline {4.2.1}task2MM1.m}{19}{subsection.4.2.1}% -\contentsline {subsubsection}{Top of task2MM1}{19}{section*.23}% -\contentsline {subsubsection}{polynomial}{19}{section*.24}% -\contentsline {subsubsection}{mm1}{19}{section*.25}% -\contentsline {subsubsection}{initialize}{20}{section*.26}% -\contentsline {subsubsection}{mm1Loop}{20}{section*.27}% -\contentsline {subsubsection}{insideLoop}{20}{section*.28}% -\contentsline {subsubsection}{createEquationSystem}{21}{section*.29}% -\contentsline {subsubsection}{rootsOfQuadraticFormula}{21}{section*.30}% -\contentsline {subsubsection}{updateApproximations}{21}{section*.31}% -\contentsline {subsubsection}{initializeEquationSystem}{22}{section*.32}% -\contentsline {subsubsection}{solveEquationSystem}{22}{section*.33}% -\contentsline {subsubsection}{createApproximatedQuadraticFormula}{23}{section*.34}% -\contentsline {subsubsection}{findRootsOfQuadraticFormula}{23}{section*.35}% -\contentsline {subsubsection}{chooseNewRoot}{23}{section*.36}% -\contentsline {subsubsection}{addZeroToIterationVector}{23}{section*.37}% -\contentsline {subsubsection}{getWorstApproximationIndex}{24}{section*.38}% -\contentsline {subsubsection}{deleteWorstApproximation}{24}{section*.39}% -\contentsline {subsection}{\numberline {4.2.2}task2MM2.m}{25}{subsection.4.2.2}% -\contentsline {subsubsection}{top of task2MM2.m}{25}{section*.40}% -\contentsline {subsubsection}{polynomial}{25}{section*.41}% -\contentsline {subsubsection}{mm2}{25}{section*.42}% -\contentsline {subsubsection}{initialize}{25}{section*.43}% -\contentsline {subsubsection}{mm2Loop}{26}{section*.44}% -\contentsline {subsubsection}{insideLoop}{26}{section*.45}% -\contentsline {subsubsection}{getABC}{26}{section*.46}% -\contentsline {subsubsection}{findRoots}{26}{section*.47}% -\contentsline {subsubsection}{chooseNewApproximation}{27}{section*.48}% -\contentsline {subsubsection}{updateApproximations}{27}{section*.49}% -\contentsline {subsubsection}{derivative}{27}{section*.50}% -\contentsline {section}{\numberline {4.3}Task 3}{28}{section.4.3}% -\contentsline {subsubsection}{Top of Task 3}{28}{section*.51}% -\contentsline {subsubsection}{polynomial}{28}{section*.52}% -\contentsline {subsubsection}{laguerre}{28}{section*.53}% -\contentsline {subsubsection}{initialize}{29}{section*.54}% -\contentsline {subsubsection}{laguerreLoop}{29}{section*.55}% -\contentsline {subsubsection}{insideLoop}{29}{section*.56}% -\contentsline {subsubsection}{calculateDerrivatives}{30}{section*.57}% -\contentsline {subsubsection}{calculateZ}{30}{section*.58}% -\contentsline {subsubsection}{chooseNewZero}{30}{section*.59}% -\contentsline {subsubsection}{updateZeros}{31}{section*.60}% -\contentsline {subsection}{\numberline {4.3.1}rootBrackering.m}{31}{subsection.4.3.1}% -\contentsline {subsubsection}{updateZeros}{31}{section*.61}% -\contentsline {subsubsection}{initializeValues}{32}{section*.62}% -\contentsline {subsubsection}{bracketingLoop}{33}{section*.63}% -\contentsline {subsection}{\numberline {4.3.2}printGraph.m}{34}{subsection.4.3.2}% -\contentsline {subsection}{\numberline {4.3.3}printComplexGraph.m}{36}{subsection.4.3.3}% +\contentsline {section}{\numberline {1.2}b) the Newton's method}{6}{section.1.2}% +\contentsline {subsection}{\numberline {1.2.1}Problem}{6}{subsection.1.2.1}% +\contentsline {subsection}{\numberline {1.2.2}Theoretical Introduction}{6}{subsection.1.2.2}% +\contentsline {subsection}{\numberline {1.2.3}Results}{7}{subsection.1.2.3}% +\contentsline {chapter}{\numberline {2}Find real and complex roots of the polynomial}{9}{chapter.2}% +\contentsline {section}{\numberline {2.1}Problem}{9}{section.2.1}% +\contentsline {section}{\numberline {2.2}Theoretical Introduction}{9}{section.2.2}% +\contentsline {subsection}{\numberline {2.2.1}MM1}{10}{subsection.2.2.1}% +\contentsline {subsection}{\numberline {2.2.2}MM2}{11}{subsection.2.2.2}% +\contentsline {section}{\numberline {2.3}Results}{12}{section.2.3}% +\contentsline {subsection}{\numberline {2.3.1}Comparison of results between MM1 and MM2}{16}{subsection.2.3.1}% +\contentsline {subsection}{\numberline {2.3.2}Comparison of results between Newton's method and MM2}{16}{subsection.2.3.2}% +\contentsline {chapter}{\numberline {3}Find real and complex roots of the polynomial using Laguerre's method}{17}{chapter.3}% +\contentsline {section}{\numberline {3.1}Problem}{17}{section.3.1}% +\contentsline {section}{\numberline {3.2}Theoretical Introduction}{17}{section.3.2}% +\contentsline {section}{\numberline {3.3}Results}{18}{section.3.3}% +\contentsline {subsection}{\numberline {3.3.1}Comparison of results between MM1 and MM2}{20}{subsection.3.3.1}% +\contentsline {chapter}{\numberline {4}Code appendix}{21}{chapter.4}% +\contentsline {section}{\numberline {4.1}Task 1}{21}{section.4.1}% +\contentsline {subsection}{\numberline {4.1.1}task1Bisection.m}{21}{subsection.4.1.1}% +\contentsline {subsubsection}{Top of task1Bisection.m}{21}{section*.4}% +\contentsline {subsubsection}{taskFunction}{21}{section*.5}% +\contentsline {subsubsection}{falsePosition}{22}{section*.6}% +\contentsline {subsubsection}{initialize}{22}{section*.7}% +\contentsline {subsubsection}{taskFunction}{22}{section*.8}% +\contentsline {subsubsection}{firstTwoIterations}{23}{section*.9}% +\contentsline {subsubsection}{falsePositionLoop}{23}{section*.10}% +\contentsline {subsubsection}{insideLoop}{24}{section*.11}% +\contentsline {subsubsection}{changeLastTwoAB}{24}{section*.12}% +\contentsline {subsubsection}{calculateZero}{25}{section*.13}% +\contentsline {subsubsection}{newSubInterval}{25}{section*.14}% +\contentsline {subsection}{\numberline {4.1.2}task1Newton.m}{25}{subsection.4.1.2}% +\contentsline {subsubsection}{Top of task1Newton.m}{25}{section*.15}% +\contentsline {subsubsection}{taskFunction}{26}{section*.16}% +\contentsline {subsubsection}{newtonMethod}{26}{section*.17}% +\contentsline {subsubsection}{initialize}{26}{section*.18}% +\contentsline {subsubsection}{newtonLoop}{26}{section*.19}% +\contentsline {subsubsection}{insideLoop}{27}{section*.20}% +\contentsline {subsubsection}{calculateZeroIterations}{27}{section*.21}% +\contentsline {subsubsection}{checkForDivergence}{27}{section*.22}% +\contentsline {section}{\numberline {4.2}Task 2}{28}{section.4.2}% +\contentsline {subsection}{\numberline {4.2.1}task2MM1.m}{28}{subsection.4.2.1}% +\contentsline {subsubsection}{Top of task2MM1}{28}{section*.23}% +\contentsline {subsubsection}{polynomial}{28}{section*.24}% +\contentsline {subsubsection}{mm1}{28}{section*.25}% +\contentsline {subsubsection}{initialize}{29}{section*.26}% +\contentsline {subsubsection}{mm1Loop}{29}{section*.27}% +\contentsline {subsubsection}{insideLoop}{29}{section*.28}% +\contentsline {subsubsection}{createEquationSystem}{30}{section*.29}% +\contentsline {subsubsection}{rootsOfQuadraticFormula}{30}{section*.30}% +\contentsline {subsubsection}{updateApproximations}{30}{section*.31}% +\contentsline {subsubsection}{initializeEquationSystem}{31}{section*.32}% +\contentsline {subsubsection}{solveEquationSystem}{31}{section*.33}% +\contentsline {subsubsection}{createApproximatedQuadraticFormula}{32}{section*.34}% +\contentsline {subsubsection}{findRootsOfQuadraticFormula}{32}{section*.35}% +\contentsline {subsubsection}{chooseNewRoot}{32}{section*.36}% +\contentsline {subsubsection}{addZeroToIterationVector}{32}{section*.37}% +\contentsline {subsubsection}{getWorstApproximationIndex}{33}{section*.38}% +\contentsline {subsubsection}{deleteWorstApproximation}{33}{section*.39}% +\contentsline {subsection}{\numberline {4.2.2}task2MM2.m}{34}{subsection.4.2.2}% +\contentsline {subsubsection}{top of task2MM2.m}{34}{section*.40}% +\contentsline {subsubsection}{polynomial}{34}{section*.41}% +\contentsline {subsubsection}{mm2}{34}{section*.42}% +\contentsline {subsubsection}{initialize}{34}{section*.43}% +\contentsline {subsubsection}{mm2Loop}{35}{section*.44}% +\contentsline {subsubsection}{insideLoop}{35}{section*.45}% +\contentsline {subsubsection}{getABC}{35}{section*.46}% +\contentsline {subsubsection}{findRoots}{35}{section*.47}% +\contentsline {subsubsection}{chooseNewApproximation}{36}{section*.48}% +\contentsline {subsubsection}{updateApproximations}{36}{section*.49}% +\contentsline {subsubsection}{derivative}{36}{section*.50}% +\contentsline {section}{\numberline {4.3}Task 3}{37}{section.4.3}% +\contentsline {subsubsection}{Top of Task 3}{37}{section*.51}% +\contentsline {subsubsection}{polynomial}{37}{section*.52}% +\contentsline {subsubsection}{laguerre}{37}{section*.53}% +\contentsline {subsubsection}{initialize}{38}{section*.54}% +\contentsline {subsubsection}{laguerreLoop}{38}{section*.55}% +\contentsline {subsubsection}{insideLoop}{38}{section*.56}% +\contentsline {subsubsection}{calculateDerrivatives}{39}{section*.57}% +\contentsline {subsubsection}{calculateZ}{39}{section*.58}% +\contentsline {subsubsection}{chooseNewZero}{39}{section*.59}% +\contentsline {subsubsection}{updateZeros}{40}{section*.60}% +\contentsline {subsection}{\numberline {4.3.1}rootBrackering.m}{40}{subsection.4.3.1}% +\contentsline {subsubsection}{updateZeros}{40}{section*.61}% +\contentsline {subsubsection}{initializeValues}{41}{section*.62}% +\contentsline {subsubsection}{bracketingLoop}{42}{section*.63}% +\contentsline {subsection}{\numberline {4.3.2}printGraph.m}{43}{subsection.4.3.2}% +\contentsline {subsection}{\numberline 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