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Research Article | Open Access

Two new generalized iteration methods for solving absolute value equations using M-matrix

Rashid Ali1( ), Ilyas Khan2, Asad Ali1, Abdullah Mohamed3
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, Hunan, China
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Research Centre, Future University in Egypt, New Cairo 11745, Egypt
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Abstract

In this paper, we present two new generalized Gauss-Seidel iteration methods for solving absolute value equations A x − | x | = b , where A is an M-matrix. Furthermore, we demonstrate their convergence under specific assumptions. Numerical tests indicate the efficiency of the suggested methods with suitable parameters.

Keywords

absolute value equationsconvergence analysisM-matrixnumerical tests
CLC number: 90C30, 65F10

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8176-8187
DOI: 10.3934/math.2022455

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Cite this article:
Ali R, Khan I, Ali A, et al. Two new generalized iteration methods for solving absolute value equations using M-matrix. AIMS Mathematics, 2022, 7(5): 8176-8187. https://doi.org/10.3934/math.2022455

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Received: 19 October 2021
Revised: 24 January 2022
Accepted: 06 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)