An implicit Hari--Zimmermann algorithm for the generalized SVD on the GPUs

31 Aug 2019Vedran NovakovićSanja Singer

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...

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