Re: Gauss-Seidel Iteration Problem - A Better Solution???

You're using dense matrices that violates one of the constraints right
away. Also, it is much more effective to use vectorized operations in
Matlab

Let A = L + D + U then write your Gauss-Seidel iterations as:
(U+D)x_{n+1} = b - L * x_n, or in Matlab syntax,

x_new = (U+D)\(b - L*x);

The mldivide (\) is smart enough to recognize purely triangular solves.

Compute U+D and L using spdiags (a sparse matrix constructor).

e = ones(n, 1); % n is your problem size
U+D is spdiags([4*e, e], 0:1, n, n) and L is spdiags(e, -1, n, n)

HTH.

.

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