Recursive versions of the Cholesky and LU decompositions
by
Krassimir Georgiev
Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria
Coauthors: Jerzy Wasniewski (Danish Center for Research and Education, UNI-C, Lyngby, Denmark)

The effective use of the cache memories of the processors is a key component of obtaining high performance algorithms and codes, including here algorithms and codes for parallel computers with shared and distributed memories. The recursive algorithms seem to be a tool for such an action. Unfortunately, worldwide used programming language FORTRAN 77 does not allow explicit recursion. The paper presents recursive versions of the Cholesky factorization algorithm for real symmetric or complex Hermitian positive definite matrices and LU factorization algorithm for general matrices using FORTRAN 90. FORTRAN 90 allows writing recursive procedures and the recursion is automatic as it is a duty of the compiler. Usually, recursion speeds up the algorithms. The recursive versions reported in the paper are some modification of the LAPACK algorithms and they transform some basic linear algebra operations from BLAS level 2 to BLAS level 3.

Date received: February 2, 2000