A generalization of the Gauss-Seidel iteration method for generalized absolute value equations

2025/05/02 by Tingting Luo, Luo, Tingting, Jiayu Liu +7 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Inertial Sensor and Navigation #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2505.01293

openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations. Convergence of the proposed method is analyzed. Numerical results are given to demonstrate the effectiveness and efficiency of the GGS method. Some results in the recent work of Edalatpour et al. \citeedhs2017 are extended.

Citations

• A monotone block coordinate descent method for solving absolute value equations
• Randomized iterative methods for generalized absolute value equations: Solvability and error bounds
• Characterization of Unique Solvability of Absolute Value Equations: An Overview, Extensions, and Future Directions
• Optimality Conditions and Numerical Algorithms for A Class of Linearly Constrained Minimax Optimization Problems
• On the unique solution of the generalized absolute value equation
• On equivalent reformulations for absolute value equations
• A generalized Newton method for absolute value equations associated with second order cones

Cited by

• Randomized iterative methods with Polyak step-size for solving generalized absolute value equations

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