Modified Hermitian and skew‐Hermitian splitting methods for non‐Hermitian positive‐definite linear systems

To further study the Hermitian and non-Hermitian splitting methods for a non-Hermitian and positive-definite matrix, we introduce a so-called lopsided Hermitian and skew-Hermitian splitting and then establish a class of lopsided Hermitian/skew-Hermitian (LHSS) methods to solve the non-Hermitian and positive-definite systems of linear equations. These methods include a two-step LHSS iteration and its inexact version, the inexact Hermitian/skew-Hermitian (ILHSS) iteration, which employs some Krylov subspace methods as its inner process. We theoretically prove that the LHSS method converges to the unique solution of the linear system for a loose restriction on the parameter α. Moreover, the contraction factor of the LHSS iteration is derived. The presented numerical examples illustrate the effectiveness of both LHSS and ILHSS iterations. Copyright © 2007 John Wiley & Sons, Ltd.

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