\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}{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 {4.3.3}printComplexGraph.m}{45}{subsection.4.3.3}%