Implementing Matrix Factorizations on the Cell B. E.
Jakub Kurzak Department of Electrical Engineering and Computer Science, University of Tennessee
Jack Dongarra Department of Electrical Engineering and Computer Science, University of Tennessee Computer Science and Mathematics Division, Oak Ridge National Laboratory School of Mathematics & School of Computer Science, Manchester University
It is clear that the impact of the multicore processors and accelerators will be ubiquitous. There are obvious advantages, however, to look at linear algebra in general and dense linear algebra in particular. This type of software is critically important to computational science across an enormous spectrum of disciplines and applications. Yet more importantly, dense linear algebra has strategic advantages as a research vehicle, because the methods and algorithms that underlie it have been so thoroughly studied and are so well understood [5, 6, 10, 17]. This chapter dissects highly optimized Cell B. E. implementations of two classic dense linear algebra computations, the Cholesky factorization and the QR factorization.