Iterative methods for solving absolute value equations

Volume 26, Issue 4, pp 322--329 http://dx.doi.org/10.22436/jmcs.026.04.01
Publication Date: December 08, 2021 Submission Date: April 05, 2021 Revision Date: July 02, 2021 Accteptance Date: September 26, 2021

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.


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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


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