The new iteration methods for solving absolute value equations

Rashid Ali; Kejia Pan

Applications of Mathematics (2023)

  • Volume: 68, Issue: 1, page 109-122
  • ISSN: 0862-7940

Abstract

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Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations A x - | x | = b , where A ∈ ℝ n × n is an M -matrix or strictly diagonally dominant matrix, b ∈ ℝ n and x ∈ ℝ n is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness of our methods.

How to cite

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Ali, Rashid, and Pan, Kejia. "The new iteration methods for solving absolute value equations." Applications of Mathematics 68.1 (2023): 109-122. <http://eudml.org/doc/299429>.

@article{Ali2023,
abstract = {Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $ Ax-|x| = b$, where $A \in \mathbb \{R\}^\{n\times n\}$ is an $M$-matrix or strictly diagonally dominant matrix, $b \in \mathbb \{R\}^\{n\}$ and $x \in \mathbb \{R\}^\{n\}$ is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness of our methods.},
author = {Ali, Rashid, Pan, Kejia},
journal = {Applications of Mathematics},
keywords = {absolute value equation; iteration method; matrix splitting; linear complementarity problem; numerical experiment},
language = {eng},
number = {1},
pages = {109-122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The new iteration methods for solving absolute value equations},
url = {http://eudml.org/doc/299429},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Ali, Rashid
AU - Pan, Kejia
TI - The new iteration methods for solving absolute value equations
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 109
EP - 122
AB - Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $ Ax-|x| = b$, where $A \in \mathbb {R}^{n\times n}$ is an $M$-matrix or strictly diagonally dominant matrix, $b \in \mathbb {R}^{n}$ and $x \in \mathbb {R}^{n}$ is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness of our methods.
LA - eng
KW - absolute value equation; iteration method; matrix splitting; linear complementarity problem; numerical experiment
UR - http://eudml.org/doc/299429
ER -

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