English

Solutions for Underdetermined Generalized Absolute Value Equations

Numerical Analysis 2025-02-18 v3 Numerical Analysis Optimization and Control

Abstract

An underdetermined generalized absolute value equation (GAVE) may have no solution, one solution, finitely many or infinitely many solutions. This paper is concerned with sufficient conditions that guarantee the existence of solutions to an underdetermined GAVE. Particularly, sufficient conditions are established for an underdetermined GAVE to have infinitely many solutions with no zero entry that possess a particular or any given sign pattern. Iterative methods are proposed for the case when the underdetermined GAVE does have a solution. Some existing results for square GAVE are also extended.

Keywords

Cite

@article{arxiv.2405.16172,
  title  = {Solutions for Underdetermined Generalized Absolute Value Equations},
  author = {Cairong Chen and Xuehua Li and Ren-Cang Li},
  journal= {arXiv preprint arXiv:2405.16172},
  year   = {2025}
}

Comments

19 pages

R2 v1 2026-06-28T16:40:05.322Z