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

2020/02/07 by Arvind K. Saibaba, Saibaba, Arvind K., Joseph Hart +3 · 1 citation
Computer Science · Decision Sciences · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2002.02812

openalex publication_date 2020/02/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

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