Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems. (English) Zbl 07547198

Shokrpour, Raheleh; Ebadi, Ghodrat

Appl. Math., Praha 67, No. 3, 319-340 (2022).

Summary: Recently, N. Huang and C. Ma in [J. Comput. Math. 34, No. 3, 300–316 (2016; Zbl 1363.65050)] proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the proposed iterative methods. Then, we study upper bounds for the spectral radius of iteration matrices and give upper bounds for the extrapolation parameter of the methods. Moreover, the optimal parameters which minimize upper bounds of the spectral radius are obtained. Finally, several numerical examples are given to show the efficiency of the presented method.

MSC:

65F10	Iterative numerical methods for linear systems
65B05	Extrapolation to the limit, deferred corrections

Keywords:

extrapolated; non-Hermitian; positive definite; skew-Hermitian; splitting; HSS iteration method

Citations:

Zbl 1363.65050

References:

[1]	Albrecht, P.; Klein, M. P., Extrapolated iterative methods for linear systems, SIAM J. Numer. Anal. 21 (1984), 192-201 · Zbl 0531.65015
[2]	Axelsson, O.; Kucherov, A., Real valued iterative methods for solving complex symmetric linear systems, Numer. Linear Algebra Appl. 7 (2000), 197-218 · Zbl 1051.65025