  The generalized singular value decomposition (GSVD) is a valuable tool that
has many applications in computational science. However, computing the GSVD for
large-scale problems is challenging. Motivated by applications in
hyper-differential sensitivity analysis (HDSA), we propose new randomized
algorithms for computing the GSVD which use randomized subspace iteration and
weighted QR factorization. Detailed error analysis is given which provides
insight into the accuracy of the algorithms and the choice of the algorithmic
parameters. We demonstrate the performance of our algorithms on test matrices
and a large-scale model problem where HDSA is used to study subsurface flow.
