Random-walk interpretations of classical iteration methods (Q1805214)

Simple probabilistic interpretations of classical Jacobi and Gauss-Seidel iteration methods for discrete Laplacian operators are given. The probability background is illustrated on three examples. The random-walk interpretation is discussed to compare convergence rates of different relaxation methods (Gauss-Seidel standard ordering, Gauss-Seidel red- black ordering, \(2 \times 2\) block Jacobi, \(2 \times 2\) block Gauss- Seidel standard ordering) for the five-point Laplacian. The procedure is extended for the nine-point Laplacian. The underrelaxation technique is discussed.