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 ∈ ℝn×n is an M-matrix or strictly diagonally dominant matrix, b ∈ ℝn and x ∈ ℝn 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.
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The authors are grateful to the editors and the anonymous referees for their helpful comments and suggestions.
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Ali, R., Pan, K. The new iteration methods for solving absolute value equations. Appl Math 68, 109–122 (2023). https://doi.org/10.21136/AM.2021.0055-21
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DOI: https://doi.org/10.21136/AM.2021.0055-21
Keywords
- absolute value equation
- iteration method
- matrix splitting
- linear complementarity problem
- numerical experiment