Geodesic
A new optimized iterative method for solving $M$-matrix linear systems
Applications of Mathematics, Tome 67 (2022) no. 3, pp. 251-272.

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In this paper, we present a new iterative method for solving a linear system, whose coefficient matrix is an $M$-matrix. This method includes four parameters that are obtained by the accelerated overrelaxation (AOR) splitting and using the Taylor approximation. First, under some standard assumptions, we establish the convergence properties of the new method. Then, by minimizing the Frobenius norm of the iteration matrix, we find the optimal parameters. Meanwhile, numerical results on test examples show the efficiency of the new proposed method in contrast with the Hermitian and skew-Hermitian splitting (HSS), AOR methods and a modified version of the AOR (QAOR) iteration.
DOI : 10.21136/AM.2021.0246-20
Classification : 65F10, 90C99
Keywords: linear system; $M$-matrix; optimal parameter; Taylor approximation; optimization 
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Fakharzadeh Jahromi, Alireza; Nasseri Shams, Nafiseh. A new optimized iterative method for solving $M$-matrix linear systems. Applications of Mathematics, Tome 67 (2022) no. 3, pp. 251-272. doi : 10.21136/AM.2021.0246-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0246-20/

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