The Gauss-Seidel Iterative Method with the Preconditioning Matrix (I + S + S_m)

摘要

We propose a preconditioned iterative method with the preconditioning matrix P_(sm) = I + S + S_m for Ax = b, where A is an irreducibly diagonal dominant Z-matrix with unit diagonal. The convergence property and the comparison theorem of the proposed method are discussed. Moreover, some numerical examples are reported to confirm the theoretical analysis.