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We present a hierarchically blocked one-sided Jacobi algorithm for thesingular value decomposition (SVD), targeting both single and multiple graphicsprocessing units (GPUs). The blocking structure reflects the levels of GPU'smemory hierarchy. The algorithm may outperform MAGMA's dgesvd, while retaininghigh relative accuracy. To this end, we developed a family of parallel pivotstrategies on GPU's shared address space, but applicable also to inter-GPUcommunication. Unlike common hybrid approaches, our algorithm in a single GPUsetting needs a CPU for the controlling purposes only, while utilizing GPU'sresources to the fullest extent permitted by the hardware. When required by theproblem size, the algorithm, in principle, scales to an arbitrary number of GPUnodes. The scalability is demonstrated by more than twofold speedup forsufficiently large matrices on a Tesla S2050 system with four GPUs vs. a singleFermi card.

A hierarchically blocked Jacobi SVD algorithm for single and multiple graphics processing units