LAWRA Linear Algebra with Recursive Algorithms

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 LDLT factorization for symmetric indefinite matrices using recursion are formulated in this paper. Performance graphs of our packed Cholesky and LDLT algorithms are presented here.