Abstract
In this paper the solution of an inverse singular value problem is considered. First the decomposition of a real square matrix A = UΣV 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 Σ 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 Σ is the diagonal matrix of singular values. Given a set σ1, ..., σn 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.
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© 2003 Springer-Verlag Berlin Heidelberg
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Politi, T. (2003). A Discrete Approach for the Inverse Singular Value Problem in Some Quadratic Group. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J.J., Zomaya, A.Y. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44862-4_14
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DOI: https://doi.org/10.1007/3-540-44862-4_14
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