Solutions for Underdetermined Generalized Absolute Value Equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913691809611776 |
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| author | Chen, Cairong Li, Xuehua Li, Ren-Cang |
| author_facet | Chen, Cairong Li, Xuehua Li, Ren-Cang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16172 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions for Underdetermined Generalized Absolute Value Equations Chen, Cairong Li, Xuehua Li, Ren-Cang Numerical Analysis Optimization and Control 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. |
| title | Solutions for Underdetermined Generalized Absolute Value Equations |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2405.16172 |