Convergence of Gauss-Seidel.

Question

I am preparing for an exam and I have an exercise type, without any example. Give the following system : $$ \begin{bmatrix} 2 & 1\\ -1 & 2\\ \end{bmatrix} *x = \begin{bmatrix} 3\\ 1\\ \end{bmatrix} $$ study the convergence of Gauss-Seidel method.I have no ideea what should I look for , so any tips wold be welcome. Thank you.

Answer 1

The convergence properties of the Gauss–Seidel method are dependent on the matrix A. Namely, the procedure is known to converge if either:

A is symmetric positive-definite or A is strictly or irreducibly diagonally dominant.

[By http://en.wikipedia.org/wiki/Gauss–Seidel_method#Convergence ]