In this paper the solution of an inverse singular value problem is considered. First the decomposition of a real square matrix A = USigmaV is introduced, where U and V are real square matrices orthogonal with respect to a particular inner product defined through a real diagonal matrix G of order n having all the elements equal to +/-1, and Sigma is a real diagonal matrix with nonnegative elements, called G-singular values. When G is the identity matrix this decomposition is the usual SVD and Sigma is the diagonal matrix of singular values. Given a set {sigma(1),...,sigma(n)} of n real positive numbers we consider the problem to find a real matrix A having them as G-singular values. Neglecting theoretical aspects of the problem, we discuss only an algorithmic issue, trying to apply a Newton type algorithm already considered for the usual inverse singular value problem.

A Discrete Approach for the Inverse Singular Value Problem in Some Quadratic Group / Politi, Tiziano. - STAMPA. - 2658:(2003), pp. 121-130. (Intervento presentato al convegno International Conference on Computational Science, ICCS2003 tenutosi a June 2-4, 2003 nel Melbourne, Australia ; St. Petersburg, Russia) [10.1007/3-540-44862-4_14].

A Discrete Approach for the Inverse Singular Value Problem in Some Quadratic Group

Tiziano Politi
2003-01-01

Abstract

In this paper the solution of an inverse singular value problem is considered. First the decomposition of a real square matrix A = USigmaV is introduced, where U and V are real square matrices orthogonal with respect to a particular inner product defined through a real diagonal matrix G of order n having all the elements equal to +/-1, and Sigma is a real diagonal matrix with nonnegative elements, called G-singular values. When G is the identity matrix this decomposition is the usual SVD and Sigma is the diagonal matrix of singular values. Given a set {sigma(1),...,sigma(n)} of n real positive numbers we consider the problem to find a real matrix A having them as G-singular values. Neglecting theoretical aspects of the problem, we discuss only an algorithmic issue, trying to apply a Newton type algorithm already considered for the usual inverse singular value problem.
2003
International Conference on Computational Science, ICCS2003
978-3-540-40195-7
A Discrete Approach for the Inverse Singular Value Problem in Some Quadratic Group / Politi, Tiziano. - STAMPA. - 2658:(2003), pp. 121-130. (Intervento presentato al convegno International Conference on Computational Science, ICCS2003 tenutosi a June 2-4, 2003 nel Melbourne, Australia ; St. Petersburg, Russia) [10.1007/3-540-44862-4_14].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/17417
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