Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis
Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis
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DOI：
10.1002/nla.2364
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发表时间：
2020-02
影响因子：
4.3
通讯作者：
A. Saibaba;Joseph L. Hart;B. V. B. Waanders-B.-V.-B.-Waanders-1863062
中科院分区：
文献类型：
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作者：
A. Saibaba;Joseph L. Hart;B. V. B. Waanders-B.-V.-B.-Waanders-1863062
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是具有挑战性的。基于超差分灵敏度分析（HDSA）中的应用，本文提出了一种基于随机子空间迭代和加权QR分解的GSVD随机化算法。给出了详细的误差分析，深入了解了算法的精度和算法参数的选择。我们在测试矩阵和大规模模型问题上展示了我们的算法的性能，其中HDSA用于研究地下流。
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.