Parallel tiled QR factorization for multicore architectures

Authors:
Alfredo Buttari;Julien Langou;Jakub Kurzak;Jack Dongarra
Affiliations:
Computer Science Dept., University of Tennessee, Knoxville;Department of Mathematical Sciences, University of Colorado at Denver and Health Sciences Center, Colorado;Computer Science Dept., University of Tennessee, Knoxville;Computer Science Dept., University of Tennessee, Knoxville and Oak Ridge National Laboratory, Oak Ridge, Tennessee and University of Manchester, UK
Venue:
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Year:
2007

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Abstract

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these new processors. Fine grain parallelism becomes a major requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data. These tasks can be dynamically scheduled for execution based on the dependencies among them and on the availability of computational resources. Compared to the standard approach, say with LAPACK, may result in an out of order execution of the tasks which will completely hide the presence of intrinsically sequential tasks in the factorization. Performance comparisons are presented with the LAPACK algorithm for QR factorization where parallelism can only be exploited at the level of the BLAS operations.