On choices of formulations of computing the generalized singular value decomposition of a matrix pair
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For the computation of the generalized singular value decomposition (GSVD) of a matrix pair (A,B) of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a generalized eigensolver can be applied to one of them and the desired GSVD components are then recovered from the computed generalized eigenpairs. Our concern in this paper is which formulation of the generalized eigenvalue problems is preferable to compute the desired GSVD components more accurately. A detailed perturbation analysis is made on the two formulations and show how to make a suitable choice between them. Numerical experiments illustrate the obtained results.
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