sor_method.txt

sor method matlab for iterative methode

% (c) 2004/2005 Universitaet Stuttgart
% Chair 'Numerische Mathematik fuer Hoechstleistungsrechner'
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\begin{exercise}{Jacobi and SOR method}{tutorial}{10}{indir02\_eng}
Write Matlab functions with the function headers
\begin{itemize}
\item[a)] \texttt{function [u,m] = solveJacobi(A, f, s, tol, max)}
\item[b)] \texttt{function [u,m] = solveSOR(A, f, s, w, tol, max)}
\end{itemize}
that solve the linear equation system $Au=f$ iteratively by using the Jacobi and the SOR method ($A$ must be a symmetric, positive definite $n \times n$ matrix). \texttt{tol} represents a given termination condition (see below), \texttt{max} is the maximum number of iterations to perform, $s$ is the iteration start vector, $w \in (0, 2)$ the so-called relaxation parameter of the SOR method. The output arguments of the function are the number of iterations performed $m$ and the approximate solution vector $u$.
\[
\text{Termination condition:} ~~ \frac{\norm{f-Au}_2}{\norm{f}_2} \leq \texttt{tol}
\]
\end{exercise}