On the strong <i>P</i>-regular splitting iterative methods for non-Hermitian linear systems

Junxiang Lu; Chengyi Zhang; Junxiang Lu; Chengyi Zhang

doi:10.3934/math.2021689

AIMS Mathematics

2021, Volume 6, Issue 11: 11879-11893. doi: 10.3934/math.2021689

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On the strong P-regular splitting iterative methods for non-Hermitian linear systems

Junxiang Lu ^{1
,
,},
Chengyi Zhang ²

1.
Department of Mathematics of School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi 710048, China
2.
School of Economics and Finance, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China

Received: 03 July 2021 Accepted: 06 August 2021 Published: 16 August 2021
MSC : 65F10, 15A15, 15F10

The strong P-regular splitting is put forward and defined for iterative methods of non-Hermitian linear systems in the paper. The strong P-regular splitting combining SOR iterative methods and relaxed SOR iterative methods are established, and conditions guaranteeing the convergence are presented. Furthermore, two numerical experiments are done to illustrate the convergence and effectiveness of our iterative methods.
- non-Hermitian positive definite matrices,
- $ P $-regular splitting,
- convergence,
- SOR methods
Citation: Junxiang Lu, Chengyi Zhang. On the strong P-regular splitting iterative methods for non-Hermitian linear systems[J]. AIMS Mathematics, 2021, 6(11): 11879-11893. doi: 10.3934/math.2021689

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Abstract

The strong P-regular splitting is put forward and defined for iterative methods of non-Hermitian linear systems in the paper. The strong P-regular splitting combining SOR iterative methods and relaxed SOR iterative methods are established, and conditions guaranteeing the convergence are presented. Furthermore, two numerical experiments are done to illustrate the convergence and effectiveness of our iterative methods.

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