Iterative methods for solving absolute value equations

Volume 26, Issue 4, pp 322--329
Publication Date: December 08, 2021 Submission Date: April 05, 2021 Revision Date: July 02, 2021 Accteptance Date: September 26, 2021
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Authors

R. Ali - School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, Hunan, P.R. China. - Department of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan. A. Ali - Department of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan. S. Iqbal - Department of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan.

Abstract

We suggest and analyze some iterative methods called Jacobi, Gauss--Seidel, SOR (successive over-relaxation), and modified Picard methods for solving absolute value equations $Ax-| x | = b$, where $A$ is an $M$-matrix, $b \in R^{n}$ is a real vector, and $x \in R^{n}$ is unknown. Furthermore, we discuss the convergence of the suggested methods under suitable assumptions and represent their performance through our numerical results. Results are very encouraging and may stimulate further research in this direction.

Share and Cite

ISRP Style

R. Ali, A. Ali, S. Iqbal, Iterative methods for solving absolute value equations, Journal of Mathematics and Computer Science, 26 (2022), no. 4, 322--329

AMA Style

Ali R., Ali A., Iqbal S., Iterative methods for solving absolute value equations. J Math Comput SCI-JM. (2022); 26(4):322--329

Chicago/Turabian Style

Ali, R., Ali, A., Iqbal, S.. "Iterative methods for solving absolute value equations." Journal of Mathematics and Computer Science, 26, no. 4 (2022): 322--329

Keywords

• Absolute value equations
• iterative methods
• $M$-matrix
• convergence
• numerical experiments

•  90C30
•  65F10
•  90C05

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