Shift-splitting iteration methods for a class of large sparse linear matrix equations

Abstract

By utilizing an inner-outer iteration strategy, a shift-splitting (SS) iteration method to solve a class of large sparse linear matrix equation AXB=C is proposed in this work. Two convergence theorems for differential forms are studied in depth. Moreover, the quasi-optimal parameters which minimize the upper bound for the spectral radius of SS iteration matrix are given. Two numerical examples illustrate the high-efficiency of SS iteration method, especially when coefficient matrices are ill-conditioned.

Keywords

• linear matrix equation
• shift-splitting iteration
• inexact iteration
• convergence analysis