A parallel, blocked, one-sided Hari--Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair $(F,G)$ is here proposed, where $F$ and $G$ have the same number of columns, and are both of the full column rank. The algorithm targets either a single graphics processing unit (GPU), or a cluster of those, performs all non-trivial computation exclusively on the GPUs, utilizes their resources to almost the full extent with data large enough, requires the minimal amount of memory to be reasonably expected, scales satisfactorily with the increase of the number of GPUs available, and guarantees the reproducible, bitwise identical output of the runs repeated over the same input and with the same number of GPUs.

中文翻译：

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GPU 上广义 SVD 的隐式 Hari-Zimmermann 算法

这里提出了一种并行的、阻塞的、单边的 Hari--Zimmermann 算法，用于实数或复数矩阵对 $(F,G)$ 的广义奇异值分解 (GSVD)，其中 $F$ 和 $G$ 有列数相同，并且都是全列排名。该算法针对单个图形处理单元 (GPU) 或一组图形处理单元，仅在 GPU 上执行所有非平凡计算，在数据足够大的情况下几乎完全利用其资源，需要最少的内存来可以合理预期，随着可用 GPU 数量的增加而令人满意地扩展，并保证在相同输入和相同数量的 GPU 上重复运行的可再现的、按位相同的输出。