Parallel Two-Sided Matrix Reduction to Band Bidiagonal Form on Multicore Architectures

The objective of this paper is to extend, in the context of multicore architectures, the concepts of tile algorithms [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 Top500 list of June 2008, 98% of the fastest parallel systems in the world were based on multicores. This confronts the scientific software community with both a daunting challenge and a unique opportunity. The challenge arises from the disturbing mismatch between the design of systems based on this new chip architecture – hundreds of thousands of nodes, a million or more cores, reduced bandwidth and memory available to cores – and the components of the traditional software stack, such as numerical libraries, on which scientific applications have relied for their accuracy and performance...

• Type: Journal
• Year: 2010
• Where: TPDS
• Authors: Hatem Ltaief, Jakub Kurzak, Jack Dongarra
• Keywords: Bidiagonal Reduction, Singular Value Decomposition, Tile Algorithms, TPDS 2010