Randomized Algorithms for Generalized Singular Value Decomposition with Application to Sensitivity Analysis

Abstract

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.