Improved convergence theorems for new Hermitian and skew-Hermitian splitting methods

Abstract

In this note, based on the previous work by Pour and Goughery (New Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems Numer. Algor. 69 (2015) 207–225), we further discuss this new Hermitian and skew-Hermitian splitting (described as NHSS) methods for non-Hermitian positive definite linear systems. Some new convergence conditions of the NHSS method are obtained, which are superior to the results in the above paper.

Keywords:

• Non-Hermitian positive definite matrix
• Hermitian matrix
• skew-Hermitian matrix
• matrix splitting
• HSS iteration
• convergence

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research of this author was supported by NSFC [grant number 1301109], Natural Science Foundations of Henan Province [grant number 15A110007] and Project of Young Core Instructor of Universities in Henan Province [grant number 2015GGJS-003].