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 codimension 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.

TAKAGI FACTORIZATION OF MATRICES DEPENDING ON PARAMETERS AND LOCATING DEGENERACIES OF SINGULAR VALUES / Dieci L.; Papini A.; Pugliese A.. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - STAMPA. - 43:(2022), pp. 1148-1161. [10.1137/21M1456273]

TAKAGI FACTORIZATION OF MATRICES DEPENDING ON PARAMETERS AND LOCATING DEGENERACIES OF SINGULAR VALUES

Papini A.;
2022

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 codimension 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.
2022
43
1148
1161
Dieci L.; Papini A.; Pugliese A.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1286486
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