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.
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Titolo: | Two-Parameter SVD: Coalescing Singular Values and Periodicity |
Autori: | |
Data di pubblicazione: | 2009 |
Rivista: | |
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 |