HSS(0): an Improved Hermitian/Skew-Hermitian Splitting Iteration
Abstract
We propose an improved version of the Hermitian/skew-Hermitian splitting (HSS) iterative method, which we call HSS(0), to solve non-Hermitian linear systems with a positive definite Hermitian part. The improvement is based on solving the Hermitian half iteration without a shift, and applying a shift only for the skew-Hermitian solve. An optimal parameter is derived analytically, and a corresponding upper bound on the convergence speed is obtained. Using a combination of analytical proofs and numerical validations, we show that HSS(0) yields a dramatically faster convergence speed than standard HSS. Furthermore, HSS(0) is much less sensitive to the choice of the parameter. Numerical experiments on a convection-diffusion model problem in two and three dimensions illustrate the high efficiency of HSS(0).
Keywords
Cite
@article{arxiv.2109.13327,
title = {HSS(0): an Improved Hermitian/Skew-Hermitian Splitting Iteration},
author = {Chen Greif and Yunhui He},
journal= {arXiv preprint arXiv:2109.13327},
year = {2021}
}
Comments
After posting this paper, we found out that the proposed method had already been published previously. See Li, Huang, and Liu, Numerical Linear Algebra with Applications, 14 (2007), pp. 217-235; Salkuyeh and Behnejad, Numerical Linear Algebra with Applications, 19 (2012), pp. 885-890