In this paper, we consider the problem to compute a special kind of singular value decomposition of a square matrix A = U Sigma V, where U and V belong to the same D-orthogonal group, i.e. they are orthogonal with respect to a real diagonal orthogonal matrix D, while Sigma is a real diagonal positive definite matrix. In this work, we propose an algebraic method and derive a continuous approach using the projected gradient technique. The differential systems given by the continuous approach are solved using a standard integration solver together with a projection technique obtained computing the D-orthogonal factor of the hyperbolic QR decomposition.

Numerical Methods for Computing the SVD in the D-orthogonal Group

PUGLIESE, Alessandro
2006

Abstract

In this paper, we consider the problem to compute a special kind of singular value decomposition of a square matrix A = U Sigma V, where U and V belong to the same D-orthogonal group, i.e. they are orthogonal with respect to a real diagonal orthogonal matrix D, while Sigma is a real diagonal positive definite matrix. In this work, we propose an algebraic method and derive a continuous approach using the projected gradient technique. The differential systems given by the continuous approach are solved using a standard integration solver together with a projection technique obtained computing the D-orthogonal factor of the hyperbolic QR decomposition.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/11687
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