An Improved SSOR-Like Preconditioner for the Non-Hermitian-Positive Definite Linear System with a Dominant Skew-Hermitian Part

doi:10.1007/s42967-024-00446-2

Abstract

Abstract: An improved SSOR-like (ISSOR-like) preconditioner is proposed for the non-Hermitian positive definite linear system with a dominant skew-Hermitian part. The upper and lower bounds on the real and imaginary parts of the eigenvalues of the ISSOR-like preconditioned matrix and the convergence property of the corresponding ISSOR-like iteration method are discussed in depth. Numerical experiments show that the ISSOR-like preconditioner can effectively accelerate preconditioned GMRES.

Key words: Non-Hermitian positive definiteness, Dominant skew-Hermitian part, Improved SSOR-like (ISSOR-like), Preconditioner, Eigenvalue distribution

Sheng-Zhong Song, Zheng-Da Huang, Bo-Han Zhang. An Improved SSOR-Like Preconditioner for the Non-Hermitian-Positive Definite Linear System with a Dominant Skew-Hermitian Part[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 2080-2096.

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