Two stage mixed-type splitting iterative methods with applications

We present a class of two stage iterative methods, called two stage mixed-type splitting (TMS) algorithm, and analyze the convergence of this method for solving large nonsingular system of equations Ax = b. Based on this new method, we establish another two stage models such as two stage (SOR, AOR, SSOR, SAOR) algorithms. The convergence of these algorithms is discussed, under the condition that A is Z-matrix. Besides, convergence is further studied for splitting of M-matrix. Numerical example is also reported to confirm the convergence analysis.