Optimizing the SVD Bidiagonalization Process for a Batch of Small Matrices

https://doi.org/10.1016/j.procs.2017.05.237Get rights and content
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Abstract

A challenging class of problems arising in many GPU applications, called batched problems, involves linear algebra operations on many small-sized matrices. We designed batched BLAS (Basic Linear Algebra Subroutines) routines, and in particular the Level-2 BLAS GEMV and the Level-3 BLAS GEMM routines, to solve them. We proposed device functions and big-tile settings in our batched BLAS design. We adopted auto-tuning to optimize different instances of GEMV routines. We illustrated our batched BLAS approach to optimize batched bi-diagonalization progressively on a K40c GPU. The optimization techniques in this paper are applicable to the other two-sided factorizations as well.

Keywords

Hardware accelerators
batched
two-sided factorization algorithms
Singular Value Problems

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