Quasi‐HSS iteration methods for non‐Hermitian positive definite linear systems of strong skew‐Hermitian parts

Abstract

Summary For large sparse non‐Hermitian positive definite linear systems, we establish exact and inexact quasi‐HSS iteration methods and discuss their convergence properties. Numerical experiments show that both iteration methods are effective and robust when they are used either as linear solvers or as matrix splitting preconditioners for the Krylov subspace iteration methods. In addition, these two iteration methods are, respectively, much more powerful than the exact and inexact HSS iteration methods, especially when the linear systems have nearly singular Hermitian parts or strongly dominant skew‐Hermitian parts, and they can be employed to solve non‐Hermitian indefinite linear systems with only mild indefiniteness.