I implemented the Gauss-Seidel method for solving a linear system of equations. My question: Is there a way to "guess" the best initial values that give the fastest convergence?
This really depends on the problem. For instance, if you are solving a linear system for each frame, you can often use the solution from the last frame as an initial guess. Can you give us more specifics about what you are trying to do?
Any reason to why you can't use the conjugated gradient method?