A Cayley-free Two-Step Algorithm for Inverse Singular Value Problems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918317086736384 |
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| author | Fan, Jiechang Shen, Weiping Luo, Yusong Lou, Enping |
| author_facet | Fan, Jiechang Shen, Weiping Luo, Yusong Lou, Enping |
| contents | In this paper, we investigate numerical solutions for inverse singular value problems (for short, ISVPs) arising in various applications. Inspired by the methodologies employed for inverse eigenvalue problems, we propose a Cayley-free two-step algorithm for solving the ISVP. Compared to the existing two-step algorithms for the ISVP, our algorithm eliminates the need for Cayley transformations and consequently avoids solving $2(m+n)$ linear systems during the computation of approximate singular vectors at each outer iteration. Under the assumption that the Jacobian matrix at a solution is nonsingular, we present a convergence analysis for the proposed algorithm and prove a cubic root-convergence rate. Numerical experiments are conducted to validate the effectiveness of our algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Cayley-free Two-Step Algorithm for Inverse Singular Value Problems Fan, Jiechang Shen, Weiping Luo, Yusong Lou, Enping Numerical Analysis Functional Analysis Optimization and Control In this paper, we investigate numerical solutions for inverse singular value problems (for short, ISVPs) arising in various applications. Inspired by the methodologies employed for inverse eigenvalue problems, we propose a Cayley-free two-step algorithm for solving the ISVP. Compared to the existing two-step algorithms for the ISVP, our algorithm eliminates the need for Cayley transformations and consequently avoids solving $2(m+n)$ linear systems during the computation of approximate singular vectors at each outer iteration. Under the assumption that the Jacobian matrix at a solution is nonsingular, we present a convergence analysis for the proposed algorithm and prove a cubic root-convergence rate. Numerical experiments are conducted to validate the effectiveness of our algorithm. |
| title | A Cayley-free Two-Step Algorithm for Inverse Singular Value Problems |
| topic | Numerical Analysis Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2602.00517 |