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Scientific Programming
Volume 17, Issue 1-2, Pages 31-42

QR Factorization for the Cell Broadband Engine

Jakub Kurzak1 and Jack Dongarra1,2,3

1Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA
2Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA
3School of Mathematics and School of Computer Science, University of Manchester, Manchester, UK

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. Modern implementations of the QR factorization, such as the one in the LAPACK library, suffer from performance limitations due to the use of matrix–vector type operations in the phase of panel factorization. These limitations can be remedied by using the idea of updating of QR factorization, rendering an algorithm, which is much more scalable and much more suitable for implementation on a multi-core processor. It is demonstrated how the potential of the cell broadband engine can be utilized to the fullest by employing the new algorithmic approach and successfully exploiting the capabilities of the chip in terms of single instruction multiple data parallelism, instruction level parallelism and thread-level parallelism.