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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} % [1 ]) @@ -481,265 +481,611 @@ l.39 ...4.1.2}task1Newton.m}{16}{subsection.4.1.2} Chapter 1. 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Info: Source file: +(epstopdf) date: 2021-12-03 04:36:42 +(epstopdf) size: 17986 bytes +(epstopdf) Output file: +(epstopdf) date: 2021-12-03 04:46:18 +(epstopdf) size: 9809 bytes +(epstopdf) Command: +(epstopdf) \includegraphics on input line 132. +Package epstopdf Info: Output file is already uptodate. + +File: task1Newtonzommedright-eps-converted-to.pdf Graphic file (type pdf) + +Package pdftex.def Info: task1Newtonzommedright-eps-converted-to.pdf used on input line 132. +(pdftex.def) Requested size: 346.29291pt x 178.16519pt. + [7 <./task1Newtonoverall-eps-converted-to.pdf> <./task1Newtonzommedleft-eps-converted-to.pdf>] [8 <./task1Newtonzommedright-eps-converted-to.pdf>] Chapter 2. -[6 +[9 -] [7] [8] [9] +] [10] +Package epstopdf Info: Source file: +(epstopdf) date: 2021-12-03 04:37:33 +(epstopdf) size: 42434 bytes +(epstopdf) Output file: +(epstopdf) date: 2021-12-03 04:48:05 +(epstopdf) size: 20938 bytes +(epstopdf) Command: +(epstopdf) \includegraphics on input line 218. 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PDF statistics: - 1078 PDF objects out of 1200 (max. 8388607) - 1007 compressed objects within 11 object streams - 598 named destinations out of 1000 (max. 500000) - 265 words of extra memory for PDF output out of 10000 (max. 10000000) + 1336 PDF objects out of 1440 (max. 8388607) + 1157 compressed objects within 12 object streams + 607 named destinations out of 1000 (max. 500000) + 385 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/ENUME/projectB/Report/report.pdf b/ENUME/projectB/Report/report.pdf index f7b915c9..1cab059f 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 0520d111..588fc543 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 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 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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}% 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