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.

中文翻译：

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应用于敏感性分析的广义奇异值分解的随机算法

广义奇异值分解 (GSVD) 是一种有价值的工具，在计算科学中有许多应用。然而，计算大规模问题的 GSVD 具有挑战性。受超微分灵敏度分析 (HDSA) 应用的启发，我们提出了新的随机算法来计算 GSVD，该算法使用随机子空间迭代和加权 QR 分解。给出了详细的误差分析，从而深入了解算法的准确性和算法参数的选择。我们展示了我们的算法在测试矩阵和大型模型问题上的性能，其中 HDSA 用于研究地下流动。