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Article

Shokrpour, Raheleh ; Ebadi, Ghodrat
Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems. (English). Applications of Mathematics, vol. 67 (2022), issue 3, pp. 319-340
MSC: 15A06, 15B48, 65B05, 65F10 | MR 4409309 | Zbl 07547198 | DOI: 10.21136/AM.2021.0256-20
Keywords:
extrapolated; non-Hermitian; positive definite; skew-Hermitian; splitting; HSS iteration method
Summary:
Recently, Na Huang and Changfeng Ma in (2016) 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.
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