
\subsection{\bf Mathematical (Matrix) Form of Gauss Seidel}

\begin{slide}

\begin{itemize}
\item Mathematically, Gauss Seidel is
\begin{displaymath}
x_i^{(k)} = \frac{\left\lbrack b_i - \sum\limits_{j<i}\, a_{i,j}\, x_j^{(k)} -
\sum\limits_{j>i}\, a_{i,j}\, x_j^{(k-1)}\right\rbrack}{a_{i,i}}
\end{displaymath}

\item In matrix language
\begin{displaymath}
\underline{x}^{(k)} = (D-L)^{-1}\ \left( U\underline{x}^{(k-1)} +
\underline{b}\right)
\end{displaymath}
 
\item where D=Diagonal, L=lower, and U=Upper parts of matrix {\bf A}

\item {\bf A}$ = D - L - U$ 
\end{itemize}

\end{slide}

