On convergence of the matrix splitting iteration paradigm for solving systems of linear equations

Abstract

For the single-step matrix splitting iteration paradigm proposed and analyzed recently by Bai (Numer. Linear Algebra Appl. 2023; e2510), we further provide a simpler and more accurate convergence result when the coefficient matrix of the linear system is a nonsingular matrix. Moreover, we demonstrate its asymptotic convergence when the coefficient matrix is an H-matrix. These results then enrich the convergence theory and enlarge the application spectrum of this paradigm.