A new optimized iterative method for solving M -matrix linear systems

Alireza Fakharzadeh Jahromi; Nafiseh Nasseri Shams

Applications of Mathematics (2022)

  • Volume: 67, Issue: 3, page 251-272
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Fakharzadeh Jahromi, Alireza, and Nasseri Shams, Nafiseh. "A new optimized iterative method for solving $M$-matrix linear systems." Applications of Mathematics 67.3 (2022): 251-272. <http://eudml.org/doc/298289>.

@article{FakharzadehJahromi2022,
abstract = {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.},
author = {Fakharzadeh Jahromi, Alireza, Nasseri Shams, Nafiseh},
journal = {Applications of Mathematics},
keywords = {linear system; $M$-matrix; optimal parameter; Taylor approximation; optimization},
language = {eng},
number = {3},
pages = {251-272},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new optimized iterative method for solving $M$-matrix linear systems},
url = {http://eudml.org/doc/298289},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Fakharzadeh Jahromi, Alireza
AU - Nasseri Shams, Nafiseh
TI - A new optimized iterative method for solving $M$-matrix linear systems
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 251
EP - 272
AB - 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.
LA - eng
KW - linear system; $M$-matrix; optimal parameter; Taylor approximation; optimization
UR - http://eudml.org/doc/298289
ER -

References

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