%0 Journal Article %J Journal of Computational Science %D 2018 %T Accelerating the SVD Bi-Diagonalization of a Batch of Small Matrices using GPUs %A Tingxing Dong %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %K Batched %K Eigenvalue and singular value problems %K hardware accelerators %K numerical linear algebra %K Two-sided factorization algorithms %X The acceleration of many small-sized linear algebra problems has become extremely challenging for current many-core architectures, and in particular GPUs. Standard interfaces have been proposed for some of these problems, called batched problems, so that they get targeted for optimization and used in a standard way in applications, calling them directly from highly optimized, standard numerical libraries, like (batched) BLAS and LAPACK. While most of the developments have been for one-sided factorizations and solvers, many important applications – from big data analytics to information retrieval, low-rank approximations for solvers and preconditioners – require two-sided factorizations, and most notably the SVD factorization. To address these needs and the parallelization challenges related to them, we developed a number of new batched computing techniques and designed batched Basic Linear Algebra Subroutines (BLAS) routines, and in particular the Level-2 BLAS GEMV and the Level-3 BLAS GEMM routines, to solve them. We propose a device functions-based methodology and big-tile setting techniques in our batched BLAS design. The different optimization techniques result in many software versions that must be tuned, for which we adopt an auto-tuning strategy to automatically derive the optimized instances of the routines. We illustrate our batched BLAS approach to optimize batched SVD bi-diagonalization progressively on GPUs. The progression is illustrated on an NVIDIA K40c GPU, and also, ported and presented on AMD Fiji Nano GPU, using AMD's Heterogeneous–Compute Interface for Portability (HIP) C++ runtime API. We demonstrate achieving 80% of the theoretically achievable peak performance for the overall algorithm, and significant acceleration of the Level-2 BLAS GEMV and Level-3 BLAS GEMM needed compared to vendor-optimized libraries on GPUs and multicore CPUs. The optimization techniques in this paper are applicable to the other two-sided factorizations as well. %B Journal of Computational Science %V 26 %P 237–245 %8 2018-05 %G eng %R https://doi.org/10.1016/j.jocs.2018.01.007