Iteration Matrix

It was relatively easy to find the eigenvalues and eigenfunctions of Jacobi's method for a simple geometry.

Gauss-Seidel it is not so easy as matrix is not symmetric. There is a nice discussion in

``Numerical Computation of Internal and External Flows,'' C. Hirsch, Wiley, 1988.

Eigenvalues of Gauss-Seidel Iteration Matrix are related to those of Jacobi Iteration by

We showed that

Therefore,