On the convergence of the MAOR method (Q1357003)

A linear system of equations \(Ax=b\) is considered, where \(A\in C^{n\times n}\), \(b,x\in C^n\), and \(A=\left(\begin{smallmatrix} D_1 &-H\\ -K & D_2\end{smallmatrix}\right)\), \(D_1\), \(D_2\) are square nonsingular diagonal matrices. The author investigates the convergence of the modified accelerated overrelaxation (MAOR) and the modified successive overrelaxation (MSOR) methods for the solution of the given system. The optimum parameters and optimum spectral radii for both methods are obtained.