\contentsline {chapter}{\numberline {1}Find all zeros of function}{3}{chapter.1}%
\contentsline {section}{\numberline {1.1}a) False position method}{3}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}Problem}{3}{subsection.1.1.1}%
\contentsline {subsection}{\numberline {1.1.2}Theoretical Introduction}{3}{subsection.1.1.2}%
\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}%