: : ABSTRACT

For about ten years now, Bo Kagstrom's Group in Umea, Sweden, Jerzy Wasniewski's team at Danish Technical University in Lyngby, Denmark, John Gunnels and I at IBM Research in Yorktown Heights have been applying recursion and New Data Structures (NDS) to increase the performance of Dense Linear Algebra (DLA) factorization algorithms. For about three years now almost all computer manufacturers have dramatically change their computer architectures which they call Multi-Core, (MC). It turns out that these new designs give poor performance for the traditional designs of DLA libraries such as LAPACK and ScaLAPACK. Recent results of Jack Dongarra's group at the Innovative Computing Laboratory in Knoxville, Tennesee have shown how to obtain high performance for DLA factorization algorithms on the Cell architecture, an example of an MC processor, but only when they used NDS. In this talk we will give some reasons why this is so. We concentrate on the unsolved problem of transforming in-place between NDS and the standard data structures of DLA, namely, Column Major (CM) or Row Major (RM) array order and packed format arrays formats for symmetric and triangular arrays. We show that fast solutions to this problem exist. The importance of this work allows existing and current level three LAPACK and ScaLAPACK codes to obtain the benefits of the new DLA codes being developed for MC processors.

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