Parallel and fully recursive multifrontal sparse Cholesky

We describe the design, implementation, and performance of a new parallel sparse Cholesky factorization code. The code uses a multifrontal factorization strategy. Operations on small dense submatrices are performed using new dense matrix subroutines that are part of the code, although the code can a...

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Bibliographic Details
Published in:Future generation computer systems Vol. 20; no. 3; pp. 425 - 440
Main Authors: Irony, Dror, Shklarski, Gil, Toledo, Sivan
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2004
Subjects:
Block layouts
Cilk
Multifrontal factorizations
Parallel Cholesky factorization
Recursive factorizations
Recursive layouts
Sparse Cholesky factorization
Parallel Cholesky factorization
Recursive factorizations
Cilk
Block layouts
Sparse Cholesky factorization
Multifrontal factorizations
Recursive layouts
ISSN:0167-739X, 1872-7115
Online Access:Get full text
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Summary:We describe the design, implementation, and performance of a new parallel sparse Cholesky factorization code. The code uses a multifrontal factorization strategy. Operations on small dense submatrices are performed using new dense matrix subroutines that are part of the code, although the code can also use the blas and lapack. The new code is recursive at both the sparse and the dense levels, it uses a novel recursive data layout for dense submatrices, and it is parallelized using Cilk, an extension of C specifically designed to parallelize recursive codes. We demonstrate that the new code performs well and scales well on SMPs. In particular, on up to 16 processors, the code outperforms two state-of-the-art message-passing codes. The scalability and high performance that the code achieves imply that recursive schedules, blocked data layouts, and dynamic scheduling are effective in the implementation of sparse factorization codes.
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ISSN:0167-739X
1872-7115
DOI:10.1016/j.future.2003.07.007