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EnglishWe consider matrix valued functions of two parameters in a simply connected region $\Omega$. We propose a new criterion to detect when such functions have coalescing singular values. For {\it generic\/} coalescings, the singular values come together in a ``double cone''-like intersection. We relate the existence of any such singularity to the periodic structure of the orthogonal factors in the singular value decomposition of the one-parameter matrix function obtained restricting to closed loops in $\Omega$. Our theoretical result is very amenable to approximate numerically the location of the singularities.
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| Titolo: | Two-Parameter SVD: Coalescing Singular Values and Periodicity |
| Autori: | |
| Data di pubblicazione: | 2009 |
| Rivista: | |
| Citazione: | Two-Parameter SVD: Coalescing Singular Values and Periodicity / Dieci L; Pugliese A. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - 31(2009), pp. 375-403. |
| Abstract: | We consider matrix valued functions of two parameters in a simply connected region $\Omega$. We propose a new criterion to detect when such functions have coalescing singular values. For {\it generic\/} coalescings, the singular values come together in a ``double cone''-like intersection. We relate the existence of any such singularity to the periodic structure of the orthogonal factors in the singular value decomposition of the one-parameter matrix function obtained restricting to closed loops in $\Omega$. Our theoretical result is very amenable to approximate numerically the location of the singularities. |
| Handle: | http://hdl.handle.net/11586/11829 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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