Abstract
Recursion leads to automatic variable blocking for dense linear algebra algorithms. The recursion transforms LAPACK level-2 algorithms into level3 codes. For this and other reasons recursion usually speeds up the algorithms.
Recursion provides a new, easy and very successful way of programming numerical linear algebra algorithms. Several algorithms for matrix factorization have been implemented and tested. Some of these algorithms are already candidates for the LAPACK library.
Recursion has also been successfully applied to the BLAS (Basic Linear Algebra Subprograms). The ATLAS system (Automatically Tuned Linear Algebra Software) uses a recursive coding of the BLAS.
The Cholesky factorization algorithm for positive definite matrices,LU factorization for general matrices, and LDL T factorization for symmetric indefinite matrices using recursion are formulated in this paper. Performance graphs of our packed Cholesky and LDL T algorithms are presented here.
This research was partially supported by the UNI•C collaboration with the IBM T.J. Watson Research Center at Yorktown Heights. The second and fifth authors was also supported by the Danish Natural Science Research Council through a grant for the EPOS project (Efficient Parallel Algorithms for Optimization and Simulation).
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Andersen, B.S., Gustavson, F., Karaivanov, A., Marinova, M., Waśniewski, J., Yalamov, P. (2001). LAWRA Linear Algebra with Recursive Algorithms. In: Sørevik, T., Manne, F., Gebremedhin, A.H., Moe, R. (eds) Applied Parallel Computing. New Paradigms for HPC in Industry and Academia. PARA 2000. Lecture Notes in Computer Science, vol 1947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-70734-4_7
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