An improved parallel singular value algorithm and its implementation for multicore hardware

  • Authors:

  • Azzam Haidar;Jakub Kurzak;Piotr Luszczek

  • Affiliations:

  • University of Tennessee, Knoxville, Tennessee;University of Tennessee, Knoxville, Tennessee;University of Tennessee, Knoxville, Tennessee

  • Venue:
  • SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
  • Year:
  • 2013

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Abstract

The enormous gap between the high-performance capabilities of today's CPUs and off-chip communication poses extreme challenges to the development of numerical software that is scalable and achieves high performance. In this article, we describe a successful methodology to address these challenges---starting with our algorithm design, through kernel optimization and tuning, and finishing with our programming model. All these lead to development of a scalable high-performance Singular Value Decomposition (SVD) solver. We developed a set of highly optimized kernels and combined them with advanced optimization techniques that feature fine-grain and cache-contained kernels, a task based approach, and hybrid execution and scheduling runtime, all of which significantly increase the performance of our SVD solver. Our results demonstrate a many-fold performance increase compared to currently available software. In particular, our software is two times faster than Intel's Math Kernel Library (MKL), a highly optimized implementation from the hardware vendor, when all the singular vectors are requested; it achieves a 5-fold speed-up when only 20% of the vectors are computed; and it is up to 10 times faster if only the singular values are required.