Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices

Abstract

For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned Hermitian and skew-Hermitian splitting iteration methods.