The computation of the partial generalized singular value decomposition (GSVD) of large-scale matrix pairs can be approached by means of iterative methods based on expanding subspaces, particularly Krylov subspaces. We consider the joint Lanczos bidiagonalization method, and analyze the feasibility of adapting the thick restart technique that is being used successfully in the context of other linear algebra problems. Numerical experiments illustrate the effectiveness of the proposed method. We also compare the new method with an alternative solution via equivalent eigenvalue problems, considering accuracy as well as computational performance. The analysis is done using a parallel implementation in the SLEPc library.

翻译：大型矩阵对的部分广义奇异值分解（GSVD）计算可通过基于扩展子空间（特别是Krylov子空间）的迭代方法实现。本文研究了联合Lanczos双对角化方法，并分析了将已在其他线性代数问题中成功应用的厚重启技术适配至该方法的可行性。数值实验验证了所提方法的有效性。此外，我们还从精度和计算性能两方面，将新方法与通过等价特征值问题求解的替代方案进行了比较。分析基于SLEPc库中的并行实现完成。