Abstract :
We discuss the general GAOR type (GGAOR) iterative method, of which special cases are the AOR, the GAOR, and the MSOR iterative methods, to solve the linear system Ax = b where A = I − L − U with L and U being general matrices. The GGAOR iteration matrix is expressed by LRΩ = (I − RL)−1[(I − Ω) + (Ω − R)L + ΩU] where R and Ω are diagonal matrices, and the MSOR iteration matrix Lωω′ = (I − Ω)−1(I − Ω + ΩU). Some basic results on the upper bounds of the spectral radii varrho(LRΩ) and varrho(Lωω′) are given when A is strictly or irreducibly diagonally dominant by rows. Based upon these results, we obtain new results on the convergence regions of the GGAOR and the MSOR iterative methods when A is an H-matrix or A has property A, and recover and improve previous ones.
