论文标题
用于敏感性分析的广义奇异值分解的随机算法
Randomized Algorithms for Generalized Singular Value Decomposition with Application to Sensitivity Analysis
论文作者
论文摘要
广义奇异值分解（GSVD）是一种有价值的工具，在计算科学中具有许多应用。但是，计算GSVD解决大规模问题是具有挑战性的。由应用超差异敏感性分析（HDSA）的应用，我们提出了用于计算使用随机子空间迭代和加权QR分解的GSVD的新的随机算法。给出了详细的错误分析，该分析提供了有关算法准确性和算法参数的选择的洞察力。我们证明了我们在测试矩阵上的算法的性能以及用于研究地下流量的大规模模型问题。
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.
