Recursive determinantal framework for testing D-stability. I
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911603079774208 |
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| author | Kushel, Olga Y. |
| author_facet | Kushel, Olga Y. |
| contents | The concept of matrix $D$-stability, introduced in 1958 by Arrow and McManus is of major importance due to the variety of its applications. However, characterization of matrix $D$-stability for dimensions $n > 4$ is considered as a hard open problem. In this paper, we propose a recursive delete/zero algorithm for testing matrix $D$-stability. The algorithm generates a binary tree of parameter-dependent matrices ${\mathbf A}_s$ and yields recurrence relations for the real and imaginary parts of $\det({\mathbf A}_s)$. These relations lead to a hierarchy of sufficient for $D$-stability conditions, expressed in terms of principal minors. Numerical experiments confirm the practical feasibility of the approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recursive determinantal framework for testing D-stability. I Kushel, Olga Y. Spectral Theory Numerical Analysis 15A12, 15A18, 15A75 The concept of matrix $D$-stability, introduced in 1958 by Arrow and McManus is of major importance due to the variety of its applications. However, characterization of matrix $D$-stability for dimensions $n > 4$ is considered as a hard open problem. In this paper, we propose a recursive delete/zero algorithm for testing matrix $D$-stability. The algorithm generates a binary tree of parameter-dependent matrices ${\mathbf A}_s$ and yields recurrence relations for the real and imaginary parts of $\det({\mathbf A}_s)$. These relations lead to a hierarchy of sufficient for $D$-stability conditions, expressed in terms of principal minors. Numerical experiments confirm the practical feasibility of the approach. |
| title | Recursive determinantal framework for testing D-stability. I |
| topic | Spectral Theory Numerical Analysis 15A12, 15A18, 15A75 |
| url | https://arxiv.org/abs/2604.16526 |