A Two-Step Iterative Method Based on Diagonal and Off-Diagonal Splitting for Solving Linear Systems

Abstract

Solving linear systems is a classical problem of engineering and numerical
analysis which has various applications in many sciences and engineering. In this
paper, we study efficient iterative methods, based on the diagonal and off-diagonal
splitting of the coefficient matrix A for solving linear system Ax = b, where A ∈ Cn×n
is nonsingular and x, b ∈ Cn×n. The new method is a two-parameter two-step method
that has some iterative methods as its special case. Numerical examples are presented
to illustrate the effectiveness of the new method.