Multi-parameters overrelaxation (MPOR) method for solving linear systems¹

Refinement of Multiparameters Overrelaxation (RMPOR) Method

“…A � M − N and A � D − k i�1 E i − F are some of the splitting of the matrix A. Using either of splittings, we can derive iterative methods which can solve the system of linear equation (1).…”

“…Recently, many researchers used the splitting A � D − k i�1 E i − F, where D is diagonal matrix of A, k i�1 E i is strictly lower triangular matrix of D − A, and F is strictly upper triangular matrix of D − A, to get the new iterative methods. Song and Dai [1] introduced multiparameters overrelaxation (MPOR) method, whose special cases involve many classical iterative methods. e convergence conditions with A being a Hermitian matrix, an L-matrix, an M-matrix, an H-matrix, and a strictly diagonally dominant matrix are derived.…”

“…Up to now, a lot of first-order stationary iterative methods are proposed. ey include the well-known methods as Jacobi, JOR, Gauss-Seidel, SOR, AOR, GAOR, TOR, and so on [1].…”