Positive Semidefinite and Positive Semidefinite Splitting Iteration Methods for Solving Nonsingular Positive Semidefinite Systems

Source abstract

This article introduces an iterative method for solving nonsingular posi tive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two positive semidefinite matrices along with an ar bitrary Hermitian positive definite shift matrix. Several conditions are established to guarantee the convergence of method and suggestions are provided for select ing the matrices involved in the desired splitting. We explore selection process of the shift matrix and determine the optimal parameter in a specific scenario. The proposed method aims to generalize previous approaches and improve the condi tions for convergence theorems. In addition, we examine two special cases of this method and compare the induced preconditioners with some state-of-art precondi tioners. Numerical examples are given to demonstrate effectiveness of the presented preconditioners.