Parallel Band Two-Sided Matrix Bidiagonalization for Multicore Architectures

Ltaief, Hatem and Kurzak, Jakub and Dongarra, Jack (2009) Parallel Band Two-Sided Matrix Bidiagonalization for Multicore Architectures. [MIMS Preprint]

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Abstract

The objective of this paper is to extend, in the context of multicore architectures, the concepts of algorithms-by-tiles [Buttari et al., 2007] for Cholesky, LU, QR factorizations to the family of two- sided factorizations. In particular, the bidiagonal reduction of a general, dense matrix is very often used as a pre-processing step for calculating the singular value decomposition. Furthermore, in the last Top500 list from June 2008, 98% of the fastest parallel systems in the world were based on multicores. The manycore trend has increasingly exacerbated the problem, and it becomes critical to eciently integrate existing or new numerical linear algebra algorithms suitable for such hardware. By exploiting the concept of algorithms-by-tiles in the multicore environment (i.e., high level of parallelism with ne granularity and high performance data representation combined with a dynamic data driven execution), the band bidiagonal reduction presented here achieves 94 G op/s on a 12000 12000 matrix with 16 Intel Tigerton 2:4 GHz processors.

Item Type: MIMS Preprint
Additional Information: Appears also as Technical Report UT-CS-08-624, Department of Computer Science, University of Tennessee, Knoxville, TN, USA, August 2008 and as LAPACK Working Note 208"
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User: Ms Lucy van Russelt
Date Deposited: 13 Jan 2009
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1211

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