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Adding table of results
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# Fdb version 3
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l.39 ...4.1.2}task1Newton.m}{25}{subsection.4.1.2}
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@ -13,21 +13,25 @@
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\BOOKMARK [2][-]{subsection.2.2.1}{MM1}{section.2.2}% 13
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\BOOKMARK [2][-]{subsection.2.2.2}{MM2}{section.2.2}% 14
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\BOOKMARK [1][-]{section.2.3}{Results}{chapter.2}% 15
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\BOOKMARK [2][-]{subsection.2.3.1}{Comparison of results between MM1 and MM2}{section.2.3}% 16
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\BOOKMARK [2][-]{subsection.2.3.2}{Comparison of results between Newton's method and MM2}{section.2.3}% 17
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\BOOKMARK [0][-]{chapter.3}{Find real and complex roots of the polynomial using Laguerre's method}{}% 18
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\BOOKMARK [1][-]{section.3.1}{Problem}{chapter.3}% 19
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\BOOKMARK [1][-]{section.3.2}{Theoretical Introduction}{chapter.3}% 20
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\BOOKMARK [1][-]{section.3.3}{Results}{chapter.3}% 21
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\BOOKMARK [2][-]{subsection.3.3.1}{Comparison of results between MM1 and MM2}{section.3.3}% 22
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\BOOKMARK [0][-]{chapter.4}{Code appendix}{}% 23
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\BOOKMARK [1][-]{section.4.1}{Task 1}{chapter.4}% 24
|
||||
\BOOKMARK [2][-]{subsection.4.1.1}{task1Bisection.m}{section.4.1}% 25
|
||||
\BOOKMARK [2][-]{subsection.4.1.2}{task1Newton.m}{section.4.1}% 26
|
||||
\BOOKMARK [1][-]{section.4.2}{Task 2}{chapter.4}% 27
|
||||
\BOOKMARK [2][-]{subsection.4.2.1}{task2MM1.m}{section.4.2}% 28
|
||||
\BOOKMARK [2][-]{subsection.4.2.2}{task2MM2.m}{section.4.2}% 29
|
||||
\BOOKMARK [1][-]{section.4.3}{Task 3}{chapter.4}% 30
|
||||
\BOOKMARK [2][-]{subsection.4.3.1}{rootBrackering.m}{section.4.3}% 31
|
||||
\BOOKMARK [2][-]{subsection.4.3.2}{printGraph.m}{section.4.3}% 32
|
||||
\BOOKMARK [2][-]{subsection.4.3.3}{printComplexGraph.m}{section.4.3}% 33
|
||||
\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
|
||||
|
||||
Binary file not shown.
Binary file not shown.
@ -97,6 +97,106 @@ It is superlinearly convergent, globally convergent and length of intervals we g
|
||||
\includegraphics[scale=0.25]{task1falsepositionzommedright.eps}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -0.17673 &-1.9421 \\
|
||||
\hline
|
||||
2 & -0.32943 &-1.7409 \\
|
||||
\hline
|
||||
3 & -0.39578 &-1.6308 \\
|
||||
\hline
|
||||
4 &-0.61812 &-1.1386 \\
|
||||
\hline
|
||||
5 &-0.76152 &-0.69765 \\
|
||||
\hline
|
||||
6 &-0.84516 &-0.38573 \\
|
||||
\hline
|
||||
7 &-0.89015 &-0.19911 \\
|
||||
\hline
|
||||
8 &-0.91304 &-0.098733 \\
|
||||
\hline
|
||||
9 & -0.92431 &-0.047922 \\
|
||||
\hline
|
||||
10 & -0.92976 & -0.02301 \\
|
||||
\hline
|
||||
11 &-0.93237 & -0.01099 \\
|
||||
\hline
|
||||
12 &-0.93362 &-0.005236 \\
|
||||
\hline
|
||||
13 &-0.93421 &-0.0024915 \\
|
||||
\hline
|
||||
14 &-0.9345 &-0.0011848 \\
|
||||
\hline
|
||||
15 &-0.93463 &-0.0005633 \\
|
||||
\hline
|
||||
16 &-0.93469 &-0.00026777 \\
|
||||
\hline
|
||||
17 &-0.93473 &-0.00012728 \\
|
||||
\hline
|
||||
18 &-0.93474 &-6.0499e-05 \\
|
||||
\hline
|
||||
19 &-0.93475 &-2.8756e-05 \\
|
||||
\hline
|
||||
20 &-0.93475 & -1.3668e-05 \\
|
||||
\hline
|
||||
21 &-0.93475 & -6.4964e-06 \\
|
||||
\hline
|
||||
22 &-0.93475 & -3.0878e-06 \\
|
||||
\hline
|
||||
23 &-0.93475 & -1.4676e-06 \\
|
||||
\hline
|
||||
24 &-0.93475 & -6.9758e-07 \\
|
||||
\hline
|
||||
25 &-0.93475 & -3.3157e-07 \\
|
||||
\hline
|
||||
26 &-0.93475 & -1.5759e-07 \\
|
||||
\hline
|
||||
27 &-0.93475 & -7.4906e-08 \\
|
||||
\hline
|
||||
28 &-0.93475 & -3.5603e-08 \\
|
||||
\hline
|
||||
29 &-0.93475 & -1.6922e-08 \\
|
||||
\hline
|
||||
30 &-0.93475 & -8.0433e-09 \\
|
||||
\hline
|
||||
31 &-0.93475 & -3.823e-09 \\
|
||||
\hline
|
||||
32 &-0.93475 & -1.8171e-09 \\
|
||||
\hline
|
||||
33 &-0.93475 & -8.6368e-10 \\
|
||||
\hline
|
||||
34 &-0.93475 & -4.1051e-10 \\
|
||||
\hline
|
||||
35 &-0.93475 & -1.9512e-10 \\
|
||||
\hline
|
||||
36 &-0.93475 & -9.2741e-11 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & 7.0323 & 0.0034663 \\
|
||||
\hline
|
||||
2 & 7.0212 & 9.0344e-05 \\
|
||||
\hline
|
||||
3 & 7.0211 & 4.6349e-05 \\
|
||||
\hline
|
||||
4 & 7.0208 & -4.3921e-05 \\
|
||||
\hline
|
||||
5 & 7.0209 & 4.8939e-11 \\
|
||||
\hline
|
||||
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\section{b) the Newton's method}
|
||||
|
||||
|
||||
@ -132,6 +232,47 @@ Newton's method is also effective if the function derrivative is far from zero,
|
||||
\includegraphics[scale=0.25]{task1Newtonzommedright.eps}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -1.25 & 1.8879 \\
|
||||
\hline
|
||||
2 & -1.0001 & 0.31855 \\
|
||||
\hline
|
||||
3 & -0.93804 & 0.015256 \\
|
||||
\hline
|
||||
4 & -0.93476 & 4.0314e-05 \\
|
||||
\hline
|
||||
5 & -0.93475 & 2.8356e-10 \\
|
||||
\hline
|
||||
6 & -0.93475 & 0 \\
|
||||
\hline
|
||||
\hline
|
||||
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & 6.25 & -0.23707 \\
|
||||
\hline
|
||||
2 & 7.0144 & -0.0019866 \\
|
||||
\hline
|
||||
3 & 7.0209 & -9.517e-08 \\
|
||||
\hline
|
||||
4 &7.0209 & 7.468e-16 \\
|
||||
\hline
|
||||
\hline
|
||||
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
|
||||
\chapter{Find real and complex roots of the polynomial}
|
||||
@ -214,6 +355,7 @@ This method is locally convergent with order of convergence equal to 1.84. It is
|
||||
|
||||
\section{Results}
|
||||
|
||||
\subsection{Graphs for MM1}
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.25]{task2mm1overall.eps}
|
||||
\end{center}
|
||||
@ -238,6 +380,7 @@ This method is locally convergent with order of convergence equal to 1.84. It is
|
||||
\includegraphics[scale=0.25]{task2mm1complexzommedup.eps}
|
||||
\end{center}
|
||||
|
||||
\subsection{Graphs for MM2}
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.25]{task2mm2overall.eps}
|
||||
\end{center}
|
||||
@ -262,6 +405,134 @@ This method is locally convergent with order of convergence equal to 1.84. It is
|
||||
\includegraphics[scale=0.25]{task2mm2complexzommedup.eps}
|
||||
\end{center}
|
||||
|
||||
\subsection{Tables for MM1}
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -1.25 & -20.32 \\
|
||||
\hline
|
||||
2 & -1.0009 & -8.0351 \\
|
||||
\hline
|
||||
3 & -0.76855 & -1.5512 \\
|
||||
\hline
|
||||
4 & -0.63496 & 0.58064 \\
|
||||
\hline
|
||||
5 & -0.67945 & -0.023155 \\
|
||||
\hline
|
||||
6 & -0.67788 & -0.00010725 \\
|
||||
\hline
|
||||
7 & -0.67787 & -8.6306e-09 \\
|
||||
\hline
|
||||
8 & -0.67787 & 0 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & 6.25 & 43.43 \\
|
||||
\hline
|
||||
2 & 6.3257 & 4.4966 \\
|
||||
\hline
|
||||
3 & 6.3341 & 0.033379 \\
|
||||
\hline
|
||||
4 & 6.3341 & -1.6916e-06 \\
|
||||
\hline
|
||||
5 & 6.3341 & -7.1942e-14 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -0.5-0.5i & 6.1847 \\
|
||||
\hline
|
||||
2 & -0.42823-0.15033i & 2.6872 \\
|
||||
\hline
|
||||
3 & -0.59202+0.094367i & 1.6012 \\
|
||||
\hline
|
||||
4 & -0.71249-0.0089336i & 0.55524 \\
|
||||
\hline
|
||||
5 & -0.67654+0.00084164i & 0.022962 \\
|
||||
\hline
|
||||
6 & -0.67787+8.4773e-06i & 0.00012412 \\
|
||||
\hline
|
||||
7 & -0.67787+3.6458e-10i & 8.3668e-09 \\
|
||||
\hline
|
||||
8 & -0.67787+9.1168e-18i & 1.3321e-16 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\subsection{Tables for MM2}
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\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 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & 6.25 & 43.43 \\
|
||||
\hline
|
||||
2 & 6.3376 & -1.8647 \\
|
||||
\hline
|
||||
3 & 6.3341 & 0.0029695 \\
|
||||
\hline
|
||||
4 & 6.3341 & 1.6294e-08 \\
|
||||
\hline
|
||||
5 & 6.3341 & -4.6896e-13 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -0.5-0.5i & 6.1847 \\
|
||||
\hline
|
||||
2 & -0.60346-0.076584i & 1.3673 \\
|
||||
\hline
|
||||
3 & -0.67709+0.001186i & 0.020767 \\
|
||||
\hline
|
||||
4 & -0.67787+1.518e-08i & 2.2673e-07 \\
|
||||
\hline
|
||||
5 & -0.67787-2.0556e-17i & 3.0035e-16 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\subsection{Comparison of results between MM1 and MM2}
|
||||
\subsection{Comparison of results between Newton's method and MM2}
|
||||
|
||||
@ -309,6 +580,61 @@ This formula is similar to the one from MM2 but also takes order of the polynomi
|
||||
\includegraphics[scale=0.25]{task3complexup.eps}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -1.25 & -20.32 \\
|
||||
\hline
|
||||
2 & -0.67905 & -0.017268 \\
|
||||
\hline
|
||||
3 & -0.67787 & -3.1489e-07 \\
|
||||
\hline
|
||||
4 & -0.67787 & 0 \\
|
||||
\hline
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -1.25 & -20.32 \\
|
||||
\hline
|
||||
2 & -0.67905 & -0.017268 \\
|
||||
\hline
|
||||
3 & -0.67787 & -3.1489e-07 \\
|
||||
\hline
|
||||
4 & -0.67787 & 0 \\
|
||||
\hline
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{| c c c |}
|
||||
\hline
|
||||
Iteration & root & f(root) \\
|
||||
\hline
|
||||
1 & -1.25 & -20.32 \\
|
||||
\hline
|
||||
2 & -0.67905 & -0.017268 \\
|
||||
\hline
|
||||
3 & -0.67787 & -3.1489e-07 \\
|
||||
\hline
|
||||
4 & -0.67787 & 0 \\
|
||||
\hline
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
|
||||
\subsection{Comparison of results between MM1 and MM2}
|
||||
|
||||
|
||||
@ -5,91 +5,95 @@
|
||||
\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}{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}%
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\contentsline {subsubsection}{initialize}{22}{section*.7}%
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||||
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||||
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|
||||
\contentsline {subsubsection}{falsePositionLoop}{23}{section*.10}%
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||||
\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}%
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||||
\contentsline {subsubsection}{taskFunction}{26}{section*.16}%
|
||||
\contentsline {subsubsection}{newtonMethod}{26}{section*.17}%
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||||
\contentsline {subsubsection}{initialize}{26}{section*.18}%
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||||
\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}%
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||||
\contentsline {subsubsection}{mm1}{28}{section*.25}%
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||||
\contentsline {subsubsection}{initialize}{29}{section*.26}%
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||||
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||||
\contentsline {subsubsection}{insideLoop}{29}{section*.28}%
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||||
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||||
\contentsline {subsubsection}{rootsOfQuadraticFormula}{30}{section*.30}%
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||||
\contentsline {subsubsection}{updateApproximations}{30}{section*.31}%
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||||
\contentsline {subsubsection}{initializeEquationSystem}{31}{section*.32}%
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||||
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||||
\contentsline {subsubsection}{createApproximatedQuadraticFormula}{32}{section*.34}%
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||||
\contentsline {subsubsection}{findRootsOfQuadraticFormula}{32}{section*.35}%
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||||
\contentsline {subsubsection}{chooseNewRoot}{32}{section*.36}%
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||||
\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}%
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||||
\contentsline {subsubsection}{polynomial}{34}{section*.41}%
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||||
\contentsline {subsubsection}{mm2}{34}{section*.42}%
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||||
\contentsline {subsubsection}{initialize}{34}{section*.43}%
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||||
\contentsline {subsubsection}{mm2Loop}{35}{section*.44}%
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||||
\contentsline {subsubsection}{insideLoop}{35}{section*.45}%
|
||||
\contentsline {subsubsection}{getABC}{35}{section*.46}%
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||||
\contentsline {subsubsection}{findRoots}{35}{section*.47}%
|
||||
\contentsline {subsubsection}{chooseNewApproximation}{36}{section*.48}%
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||||
\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 {4.3.3}printComplexGraph.m}{45}{subsection.4.3.3}%
|
||||
\contentsline {section}{\numberline {1.2}b) the Newton's method}{8}{section.1.2}%
|
||||
\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}%
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||||
\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}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\contentsline {subsubsection}{initialize}{30}{section*.18}%
|
||||
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|
||||
\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}%
|
||||
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|
||||
\contentsline {subsubsection}{mm1}{32}{section*.25}%
|
||||
\contentsline {subsubsection}{initialize}{33}{section*.26}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\contentsline {section}{\numberline {4.3}Task 3}{41}{section.4.3}%
|
||||
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|
||||
\contentsline {subsubsection}{polynomial}{41}{section*.52}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\contentsline {subsubsection}{chooseNewZero}{43}{section*.59}%
|
||||
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|
||||
\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}%
|
||||
|
||||
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Reference in New Issue
Block a user