Out-of-Core Implementations of Cholesky Factorization: Loop-Based versus Recursive Algorithms

Authors:
Natacha Béreux
Affiliations:
natacha.bereux@edf.fr
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2008

Citing 0
Cited 3

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Abstract

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.