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, requires the minimal amount of memory to be reasonably expected, scales acceptably 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.

并行，块状，单面Hari-Zimmermann算法，用于对实或复矩阵对进行广义奇异值分解（GSVD） $（F，G）$这里建议使用F，其中F和G的列数相同，并且都是完整的列级。该算法以单个图形处理单元（GPU）或其中的一个集群为目标，专门在GPU上执行所有非平凡的计算，需要合理预期的最小内存量，随着内存数量的增加而可接受地扩展可用的GPU，并保证在相同的输入和相同数量的GPU上重复运行的可重复生成的按位相同输出。