Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems

Raheleh Shokrpour; Ghodrat Ebadi

Applications of Mathematics (2022)

  • Volume: 67, Issue: 3, page 319-340
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Shokrpour, Raheleh, and Ebadi, Ghodrat. "Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems." Applications of Mathematics 67.3 (2022): 319-340. <http://eudml.org/doc/297868>.

@article{Shokrpour2022,
abstract = {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.},
author = {Shokrpour, Raheleh, Ebadi, Ghodrat},
journal = {Applications of Mathematics},
keywords = {extrapolated; non-Hermitian; positive definite; skew-Hermitian; splitting; HSS iteration method},
language = {eng},
number = {3},
pages = {319-340},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems},
url = {http://eudml.org/doc/297868},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Shokrpour, Raheleh
AU - Ebadi, Ghodrat
TI - Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 319
EP - 340
AB - 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.
LA - eng
KW - extrapolated; non-Hermitian; positive definite; skew-Hermitian; splitting; HSS iteration method
UR - http://eudml.org/doc/297868
ER -

References

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