\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 [1][-]{section.1.4}{Results}{chapter.1}% 7
\BOOKMARK [0][-]{chapter.2}{Problem 2 - Solving a system of n linear equations - indicated method}{}% 8
\BOOKMARK [1][-]{section.2.1}{Problem}{chapter.2}% 9
\BOOKMARK [1][-]{section.2.2}{Theoretical Introduction}{chapter.2}% 10
\BOOKMARK [2][-]{subsection.2.2.1}{Transform matrix into upper-triangular matrix}{section.2.2}% 11
\BOOKMARK [2][-]{subsection.2.2.2}{Backward substitution}{section.2.2}% 12
\BOOKMARK [2][-]{subsection.2.2.3}{Partial Pivoting}{section.2.2}% 13
\BOOKMARK [1][-]{section.2.3}{Results}{chapter.2}% 14
\BOOKMARK [2][-]{subsection.2.3.1}{2a\)}{section.2.3}% 15
\BOOKMARK [2][-]{subsection.2.3.2}{2b\)}{section.2.3}% 16
\BOOKMARK [1][-]{section.2.4}{Discussion of results}{chapter.2}% 17
\BOOKMARK [2][-]{subsection.2.4.1}{Errors in b\)}{section.2.4}% 18
\BOOKMARK [0][-]{chapter.3}{Problem 3 - Solving a system of n linear equations - iterative algorithm}{}% 19
\BOOKMARK [1][-]{section.3.1}{Problem}{chapter.3}% 20
\BOOKMARK [1][-]{section.3.2}{Theoretical introduction}{chapter.3}% 21
\BOOKMARK [2][-]{subsection.3.2.1}{Procedure}{section.3.2}% 22
\BOOKMARK [1][-]{section.3.3}{Results}{chapter.3}% 23
\BOOKMARK [2][-]{subsection.3.3.1}{Jacobi method result}{section.3.3}% 24
\BOOKMARK [2][-]{subsection.3.3.2}{Gauss-Seidel method result}{section.3.3}% 25
\BOOKMARK [1][-]{section.3.4}{Discussion of results}{chapter.3}% 26
\BOOKMARK [2][-]{subsection.3.4.1}{Comparison based on table}{section.3.4}% 27
\BOOKMARK [2][-]{subsection.3.4.2}{Convergence}{section.3.4}% 28
\BOOKMARK [0][-]{chapter.4}{Problem 4 - QR method of finding eigenvalues}{}% 29
\BOOKMARK [1][-]{section.4.1}{Problem}{chapter.4}% 30
\BOOKMARK [1][-]{section.4.2}{Theoretical introduction}{chapter.4}% 31
\BOOKMARK [2][-]{subsection.4.2.1}{Eigenvalues}{section.4.2}% 32
\BOOKMARK [2][-]{subsection.4.2.2}{QR method for finding eigenvalues}{section.4.2}% 33
\BOOKMARK [1][-]{section.4.3}{Results}{chapter.4}% 34
\BOOKMARK [2][-]{subsection.4.3.1}{Starting matrix}{section.4.3}% 35
\BOOKMARK [2][-]{subsection.4.3.2}{QR method with no shifts}{section.4.3}% 36
\BOOKMARK [2][-]{subsection.4.3.3}{QR method with shifts}{section.4.3}% 37
\BOOKMARK [1][-]{section.4.4}{Discussion of the result}{chapter.4}% 38
\BOOKMARK [2][-]{subsection.4.4.1}{Plot}{section.4.4}% 39
\BOOKMARK [2][-]{subsection.4.4.2}{Shift method superiority}{section.4.4}% 40
\BOOKMARK [0][-]{chapter.5}{Code appendix}{}% 41
\BOOKMARK [1][-]{section.5.1}{Task 1 Code}{chapter.5}% 42
\BOOKMARK [2][-]{subsection.5.1.1}{Find macheps}{section.5.1}% 43
\BOOKMARK [2][-]{subsection.5.1.2}{Display results}{section.5.1}% 44
\BOOKMARK [1][-]{section.5.2}{Task 2 Code}{chapter.5}% 45
\BOOKMARK [2][-]{subsection.5.2.1}{Main function}{section.5.2}% 46
\BOOKMARK [2][-]{subsection.5.2.2}{checkIfMatrixIsSquareMatrix}{section.5.2}% 47
\BOOKMARK [2][-]{subsection.5.2.3}{gaussianEliminationWithPartialPivoting}{section.5.2}% 48
\BOOKMARK [2][-]{subsection.5.2.4}{partialPivoting}{section.5.2}% 49
\BOOKMARK [2][-]{subsection.5.2.5}{partialPivotingSwapOneRow}{section.5.2}% 50
\BOOKMARK [2][-]{subsection.5.2.6}{swapRowMatrix}{section.5.2}% 51
\BOOKMARK [2][-]{subsection.5.2.7}{swapValueVector}{section.5.2}% 52
\BOOKMARK [2][-]{subsection.5.2.8}{gaussianElimination}{section.5.2}% 53
\BOOKMARK [2][-]{subsection.5.2.9}{substractRows}{section.5.2}% 54
\BOOKMARK [2][-]{subsection.5.2.10}{backSubstitutionPhase}{section.5.2}% 55
\BOOKMARK [2][-]{subsection.5.2.11}{iterativeResidualCorrection}{section.5.2}% 56
\BOOKMARK [2][-]{subsection.5.2.12}{improveSolution}{section.5.2}% 57
\BOOKMARK [2][-]{subsection.5.2.13}{plotErrorsGaussian}{section.5.2}% 58
\BOOKMARK [1][-]{section.5.3}{Task 3 Code}{chapter.5}% 59
\BOOKMARK [2][-]{subsection.5.3.1}{initializeValues}{section.5.3}% 60
\BOOKMARK [2][-]{subsection.5.3.2}{decomposeMatrix}{section.5.3}% 61
\BOOKMARK [2][-]{subsection.5.3.3}{jacobiLoop}{section.5.3}% 62
\BOOKMARK [2][-]{subsection.5.3.4}{jacobiInsideLoop}{section.5.3}% 63
\BOOKMARK [2][-]{subsection.5.3.5}{jacobiEquation}{section.5.3}% 64
\BOOKMARK [2][-]{subsection.5.3.6}{gaussSeidelLoop}{section.5.3}% 65
\BOOKMARK [2][-]{subsection.5.3.7}{gaussiInsideLoop}{section.5.3}% 66
\BOOKMARK [2][-]{subsection.5.3.8}{gaussSeidelEquation}{section.5.3}% 67
\BOOKMARK [2][-]{subsection.5.3.9}{checkError}{section.5.3}% 68
\BOOKMARK [2][-]{subsection.5.3.10}{endOfLoop}{section.5.3}% 69
\BOOKMARK [2][-]{subsection.5.3.11}{dispFinalResults}{section.5.3}% 70
\BOOKMARK [2][-]{subsection.5.3.12}{plotIterations}{section.5.3}% 71
\BOOKMARK [1][-]{section.5.4}{Task 4 Code}{chapter.5}% 72
\BOOKMARK [2][-]{subsection.5.4.1}{Gram-Schmid algorithm}{section.5.4}% 73
\BOOKMARK [2][-]{subsection.5.4.2}{task4}{section.5.4}% 74
\BOOKMARK [2][-]{subsection.5.4.3}{QRNoShifts}{section.5.4}% 75
\BOOKMARK [2][-]{subsection.5.4.4}{QRShifts}{section.5.4}% 76
\BOOKMARK [2][-]{subsection.5.4.5}{task4Plot}{section.5.4}% 77
\BOOKMARK [2][-]{subsection.5.4.6}{Matrix generation}{section.5.4}% 78