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
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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
MSC
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