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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| Vydáno v: | Future generation computer systems Ročník 20; číslo 3; s. 425 - 440 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.04.2004
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| ISSN: | 0167-739X, 1872-7115 |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Irony, Dror Toledo, Sivan Shklarski, Gil |
| Author_xml | – sequence: 1 givenname: Dror surname: Irony fullname: Irony, Dror – sequence: 2 givenname: Gil surname: Shklarski fullname: Shklarski, Gil – sequence: 3 givenname: Sivan surname: Toledo fullname: Toledo, Sivan email: stoledo@tau.ac.il |
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| Keywords | Parallel Cholesky factorization Recursive factorizations Cilk Block layouts Sparse Cholesky factorization Multifrontal factorizations Recursive layouts |
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| SubjectTerms | Block layouts Cilk Multifrontal factorizations Parallel Cholesky factorization Recursive factorizations Recursive layouts Sparse Cholesky factorization |
| Title | Parallel and fully recursive multifrontal sparse Cholesky |
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