Béreux, Natacha Out-of-core implementations of Cholesky factorization: loop-based versus recursive algorithms. (English) Zbl 1176.65024 SIAM J. Matrix Anal. Appl. 30, No. 4, 1302-1319 (2008). Summary: We compare, in the same framework, out-of-core implementations of the Cholesky factorization algorithm. The candidate implementations are the classical blocked left-looking variant and a more recent recursive formulation. Both have been implemented for real positive definite matrices: the former in the parallel out-of-core linear algebra package (POOCLAPACK) library and the latter in the scalable out-of-core linear algebra computations (SOLAR) library. We perform a theoretical analysis of the amount of input/output (I/O) operations required by each variant. We consider alternatives for the left-looking algorithm: the one-tile and two-tiles approaches. We show that when main memory is restricted, the one-tile approach yields less I/O volume. We then show that the left-looking implementation requires less I/O volume than the recursive variant. We have implemented all for complex matrices, and we report on numerical experiments. MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 65Y20 Complexity and performance of numerical algorithms Keywords:Cholesky factorization; out-of-core algorithms; numerical experiments Software:POOCLAPACK; BLAS; PLAPACK; SOLAR; SOLAR PDFBibTeX XMLCite \textit{N. Béreux}, SIAM J. Matrix Anal. Appl. 30, No. 4, 1302--1319 (2008; Zbl 1176.65024) Full Text: DOI