\BOOKMARK [0][-]{chapter.1}{Problem 1 - Finding machine epsilion}{}% 1
\BOOKMARK [1][-]{section.1.1}{Problem}{chapter.1}% 2
\BOOKMARK [1][-]{section.1.2}{Theoretical Introduction}{chapter.1}% 3
\BOOKMARK [2][-]{subsection.1.2.1}{Definition of machine epsilion}{section.1.2}% 4
\BOOKMARK [2][-]{subsection.1.2.2}{Practical applications of machine epsilion}{section.1.2}% 5
\BOOKMARK [1][-]{section.1.3}{Solution}{chapter.1}% 6
\BOOKMARK [2][-]{subsection.1.3.1}{Matlab code}{section.1.3}% 7
\BOOKMARK [1][-]{section.1.4}{Discussion of the result}{chapter.1}% 8
\BOOKMARK [0][-]{chapter.2}{Problem 2 - Solving a system of n linear equations - indicated method}{}% 9
\BOOKMARK [1][-]{section.2.1}{Problem}{chapter.2}% 10
\BOOKMARK [1][-]{section.2.2}{Theoretical Introduction}{chapter.2}% 11
\BOOKMARK [2][-]{subsection.2.2.1}{Transform matrix into upper-triangular matrix}{section.2.2}% 12
\BOOKMARK [2][-]{subsection.2.2.2}{Backward substitution}{section.2.2}% 13
\BOOKMARK [2][-]{subsection.2.2.3}{Partial Pivoting}{section.2.2}% 14
\BOOKMARK [1][-]{section.2.3}{Solution}{chapter.2}% 15
\BOOKMARK [1][-]{section.2.4}{Discussion of the result}{chapter.2}% 16
\BOOKMARK [0][-]{chapter.3}{Problem 3 - Solving a system of n linear equations - iterative algorithm}{}% 17
\BOOKMARK [1][-]{section.3.1}{Problem}{chapter.3}% 18
\BOOKMARK [1][-]{section.3.2}{Theoretical introduction}{chapter.3}% 19
\BOOKMARK [2][-]{subsection.3.2.1}{Procedure}{section.3.2}% 20
\BOOKMARK [1][-]{section.3.3}{Solution}{chapter.3}% 21
\BOOKMARK [1][-]{section.3.4}{Discussion of the result}{chapter.3}% 22
\BOOKMARK [0][-]{chapter.4}{Problem 4 - QR method of finding eigenvalues}{}% 23
\BOOKMARK [1][-]{section.4.1}{Problem}{chapter.4}% 24
\BOOKMARK [1][-]{section.4.2}{Theoretical introduction}{chapter.4}% 25
\BOOKMARK [1][-]{section.4.3}{Solution}{chapter.4}% 26
\BOOKMARK [1][-]{section.4.4}{Discussion of the result}{chapter.4}% 27
\BOOKMARK [0][-]{chapter.5}{Code appendix}{}% 28
\BOOKMARK [1][-]{section.5.1}{Task 2 Code}{chapter.5}% 29
\BOOKMARK [2][-]{subsection.5.1.1}{Main function}{section.5.1}% 30
\BOOKMARK [2][-]{subsection.5.1.2}{checkIfMatrixIsSquareMatrix}{section.5.1}% 31
\BOOKMARK [2][-]{subsection.5.1.3}{gaussianEliminationWithPartialPivoting}{section.5.1}% 32
\BOOKMARK [2][-]{subsection.5.1.4}{partialPivoting}{section.5.1}% 33
\BOOKMARK [2][-]{subsection.5.1.5}{partialPivotingSwapOneRow}{section.5.1}% 34
\BOOKMARK [2][-]{subsection.5.1.6}{swapRowMatrix}{section.5.1}% 35
\BOOKMARK [2][-]{subsection.5.1.7}{swapValueVector}{section.5.1}% 36
\BOOKMARK [2][-]{subsection.5.1.8}{gaussianElimination}{section.5.1}% 37
\BOOKMARK [2][-]{subsection.5.1.9}{substractRows}{section.5.1}% 38
\BOOKMARK [2][-]{subsection.5.1.10}{backSubstitutionPhase}{section.5.1}% 39
\BOOKMARK [2][-]{subsection.5.1.11}{iterativeResidualCorrection}{section.5.1}% 40
\BOOKMARK [2][-]{subsection.5.1.12}{improveSolution}{section.5.1}% 41