Solutions for underdetermined generalized absolute value equations

Cairong Chen

doi:10.1016/j.laa.2025.10.027

Solutions for underdetermined generalized absolute value equations

2025-10-01

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DOI：10.1016/j.laa.2025.10.027

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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. Some existing results for square GAVE are also extended. It is noted that some of the proofs are constructive and lead to iterative schemes that can solve the underdetermined GAVE in question. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Keywords:

Underdetermined linear system

Underdetermined generalized absolute value equations

Existence of solutions

Iterative methods

Solutions for underdetermined generalized absolute value equations

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