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For the computation of the generalized singular value decomposition (GSVD) ofa large matrix pair $(A,B)$ of full column rank, the GSVD is commonlyformulated as two mathematically equivalent generalized eigenvalue problems, sothat a generalized eigensolver can be applied to one of them and the desiredGSVD components are then recovered from the computed generalized eigenpairs.Our concern in this paper is, in finite precision arithmetic, which generalizedeigenvalue formulation is numerically preferable to compute the desired GSVDcomponents more accurately. We make a detailed perturbation analysis on the twoformulations and show how to make a suitable choice between them. Numericalexperiments illustrate the results obtained.

On choices of formulations of computing the generalized singular value decomposition of a large matrix pair