mirror of
https://github.com/kuhyx/WUT_Computer_Science.git
synced 2026-07-06 08:53:01 +02:00
64 lines
5.0 KiB
TeX
64 lines
5.0 KiB
TeX
\contentsline {chapter}{\numberline {1}Problem 1 - Finding machine epsilion}{3}{chapter.1}%
|
|
\contentsline {section}{\numberline {1.1}Problem}{3}{section.1.1}%
|
|
\contentsline {section}{\numberline {1.2}Theoretical Introduction}{3}{section.1.2}%
|
|
\contentsline {subsection}{\numberline {1.2.1}Definition of machine epsilion}{3}{subsection.1.2.1}%
|
|
\contentsline {subsection}{\numberline {1.2.2}Practical applications of machine epsilion}{3}{subsection.1.2.2}%
|
|
\contentsline {section}{\numberline {1.3}Solution}{4}{section.1.3}%
|
|
\contentsline {subsection}{\numberline {1.3.1}Matlab code}{4}{subsection.1.3.1}%
|
|
\contentsline {section}{\numberline {1.4}Discussion of the result}{4}{section.1.4}%
|
|
\contentsline {chapter}{\numberline {2}Problem 2 - Solving a system of n linear equations - indicated method}{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}Transform matrix into upper-triangular matrix}{6}{subsection.2.2.1}%
|
|
\contentsline {subsubsection}{Starting conditions}{6}{section*.2}%
|
|
\contentsline {subsubsection}{Zeroing first column}{7}{section*.3}%
|
|
\contentsline {subsubsection}{Zeroing second column}{7}{section*.4}%
|
|
\contentsline {subsubsection}{Zeroing next columns}{7}{section*.5}%
|
|
\contentsline {subsection}{\numberline {2.2.2}Backward substitution}{8}{subsection.2.2.2}%
|
|
\contentsline {subsection}{\numberline {2.2.3}Partial Pivoting}{8}{subsection.2.2.3}%
|
|
\contentsline {section}{\numberline {2.3}Solution}{9}{section.2.3}%
|
|
\contentsline {section}{\numberline {2.4}Discussion of the result}{9}{section.2.4}%
|
|
\newpage
|
|
\contentsline {chapter}{\numberline {3}Problem 3 - Solving a system of n linear equations - iterative algorithm}{11}{chapter.3}%
|
|
\contentsline {section}{\numberline {3.1}Problem}{11}{section.3.1}%
|
|
\contentsline {section}{\numberline {3.2}Theoretical introduction}{11}{section.3.2}%
|
|
\contentsline {subsection}{\numberline {3.2.1}Procedure}{12}{subsection.3.2.1}%
|
|
\contentsline {subsubsection}{Decomposing matrix}{12}{section*.6}%
|
|
\contentsline {subsubsection}{Jacobi's method}{13}{section*.7}%
|
|
\contentsline {paragraph}{Converging}{13}{section*.8}%
|
|
\contentsline {subsubsection}{Gauss-Seidel method}{13}{section*.9}%
|
|
\contentsline {paragraph}{Converging}{15}{section*.10}%
|
|
\contentsline {subsubsection}{Stop tests}{15}{section*.11}%
|
|
\contentsline {subsubsection}{\textbf {A} and \textbf {b}}{15}{section*.12}%
|
|
\contentsline {section}{\numberline {3.3}Solution}{16}{section.3.3}%
|
|
\contentsline {section}{\numberline {3.4}Discussion of the result}{16}{section.3.4}%
|
|
\contentsline {chapter}{\numberline {4}Problem 4 - QR method of finding eigenvalues}{17}{chapter.4}%
|
|
\contentsline {section}{\numberline {4.1}Problem}{17}{section.4.1}%
|
|
\contentsline {section}{\numberline {4.2}Theoretical introduction}{17}{section.4.2}%
|
|
\contentsline {section}{\numberline {4.3}Solution}{17}{section.4.3}%
|
|
\contentsline {section}{\numberline {4.4}Discussion of the result}{17}{section.4.4}%
|
|
\contentsline {chapter}{\numberline {5}Code appendix}{18}{chapter.5}%
|
|
\contentsline {section}{\numberline {5.1}Task 2 Code}{18}{section.5.1}%
|
|
\contentsline {subsection}{\numberline {5.1.1}Main function}{18}{subsection.5.1.1}%
|
|
\contentsline {subsection}{\numberline {5.1.2}checkIfMatrixIsSquareMatrix}{18}{subsection.5.1.2}%
|
|
\contentsline {subsection}{\numberline {5.1.3}gaussianEliminationWithPartialPivoting}{20}{subsection.5.1.3}%
|
|
\contentsline {subsection}{\numberline {5.1.4}partialPivoting}{20}{subsection.5.1.4}%
|
|
\contentsline {subsection}{\numberline {5.1.5}partialPivotingSwapOneRow}{20}{subsection.5.1.5}%
|
|
\contentsline {subsection}{\numberline {5.1.6}swapRowMatrix}{20}{subsection.5.1.6}%
|
|
\contentsline {subsection}{\numberline {5.1.7}swapValueVector}{21}{subsection.5.1.7}%
|
|
\contentsline {subsection}{\numberline {5.1.8}gaussianElimination}{21}{subsection.5.1.8}%
|
|
\contentsline {subsection}{\numberline {5.1.9}substractRows}{21}{subsection.5.1.9}%
|
|
\contentsline {subsection}{\numberline {5.1.10}backSubstitutionPhase}{22}{subsection.5.1.10}%
|
|
\contentsline {subsection}{\numberline {5.1.11}iterativeResidualCorrection}{22}{subsection.5.1.11}%
|
|
\contentsline {subsection}{\numberline {5.1.12}improveSolution}{22}{subsection.5.1.12}%
|
|
\contentsline {section}{\numberline {5.2}Task 3e code}{23}{section.5.2}%
|
|
\contentsline {subsection}{\numberline {5.2.1}jacobiMethod}{23}{subsection.5.2.1}%
|
|
\contentsline {subsection}{\numberline {5.2.2}initializeValues}{23}{subsection.5.2.2}%
|
|
\contentsline {subsection}{\numberline {5.2.3}decomposeMatrix}{23}{subsection.5.2.3}%
|
|
\contentsline {subsection}{\numberline {5.2.4}jacobiLoop}{24}{subsection.5.2.4}%
|
|
\contentsline {subsection}{\numberline {5.2.5}jacobiInsideLoop}{24}{subsection.5.2.5}%
|
|
\contentsline {subsection}{\numberline {5.2.6}jacobiEquation}{24}{subsection.5.2.6}%
|
|
\contentsline {subsection}{\numberline {5.2.7}checkError}{24}{subsection.5.2.7}%
|
|
\contentsline {subsection}{\numberline {5.2.8}endOfLoop}{25}{subsection.5.2.8}%
|
|
\contentsline {subsection}{\numberline {5.2.9}dispFinalResults}{25}{subsection.5.2.9}%
|