  For the computation of the generalized singular value decomposition (GSVD) of
a large 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, in finite precision arithmetic, which generalized
eigenvalue formulation is numerically preferable to compute the desired GSVD
components more accurately. We make a detailed perturbation analysis on the two
formulations and show how to make a suitable choice between them. Numerical
experiments illustrate the results obtained.
