Asymmetric Hermitian and skew-Hermitian splitting methods for positive definite linear systems

Abstract

In this paper, efficient iterative methods for the large sparse non-Hermitian positive definite systems of linear equations, based on the Hermitian and skew-Hermitian splitting of the coefficient matrix, are studied. These methods include an asymmetric Hermitian/skew-Hermitian (AHSS) iteration and its inexact version, the inexact asymmetric Hermitian/skew-Hermitian (IAHSS) iteration, which employs some Krylov subspace methods as its inner process. We theoretically study the convergence properties of the AHSS method and the IAHSS method. Moreover, the contraction factor of the AHSS iteration is derived. Numerical examples illustrating the effectiveness of both AHSS and IAHSS iterations are presented.