RANDOM-WALK INTERPRETATIONS OF CLASSICAL ITERATION METHODS

We give a simple framework for computing relative convergence rates fo r relaxation methods with discrete Laplace operators (five point or ni ne point). This gives relations between the convergence rate for Jacob i, point Gauss Seidel, and various block relaxation strategies, essent ially by inspection. The framework is a random walk interpretation of Jacobi relaxation that extends to these other relaxation methods.