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arXiv · 2110.15918

Takagi factorization of matrices depending on parameters and locating degeneracies of singular values

Luca Dieci·Alessandra Papini·Alessandro Pugliese
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Abstract

In this work we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the concerns caused by having either a singular value equal to $0$ or multiple singular values. For these phenomena, we give theoretical results showing that their co-dimension is $2$, and we further develop and test numerical methods to locate in parameter space values where these occurrences take place. Numerical study of the density of these occurrences is performed.

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Luca Dieci, Alessandra Papini, Alessandro Pugliese. 2021-10-29. Takagi factorization of matrices depending on parameters and locating degeneracies of singular values. https://doi.org/10.1137/21m1456273

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