Further study on two fixed point iterative schemes for absolute value equations
Jiayu Liu, Tingting Luo, Cairong Chen
TL;DR
This paper analyzes two iterative methods for solving absolute value equations, providing convergence proofs, solvability conditions, optimal parameters, and numerical validation of the methods' effectiveness.
Contribution
It introduces and analyzes two new iterative schemes for AVE, including convergence criteria, solvability conditions, and optimal parameters, with numerical validation.
Findings
Convergence of the two iterative schemes is established.
New sufficient conditions for the unique solvability of AVE are provided.
Numerical results confirm the effectiveness of the proposed methods.
Abstract
In this paper, we reconsider two new iterative methods for solving absolute value equations (AVE), which is proposed by Ali and Pan (Jpn. J. Ind. Appl. Math. 40: 303--314, 2023). Convergence results of the two iterative schemes and new sufficient conditions for the unique solvability of AVE are presented. In addition, for a special case, the optimal iteration parameters of the two algorithms are analyzed, respectively. Numerical results demonstrate our claims.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Iterative Methods for Nonlinear Equations