A parallel algorithm for sparse unsymmetric Lu factorization:
Abstract: "This thesis presents a parallel algorithm for the direct LU factorization of general unsymmetric sparse matrices. The algorithm, D2, is based on a new nondeterministic parallel pivot search that finds a compatible pivot set S of size m, followed by a parallel rank-m update. These two...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Urbana, Ill.
1989
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| Series: | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report
907 |
| Subjects: | |
| Summary: | Abstract: "This thesis presents a parallel algorithm for the direct LU factorization of general unsymmetric sparse matrices. The algorithm, D2, is based on a new nondeterministic parallel pivot search that finds a compatible pivot set S of size m, followed by a parallel rank-m update. These two steps alternate until switching to dense matrix code or until the matrix is factored. The algorithm is based on a shared-memory MIMD model and takes advantage of both concurrency and (gather-scatter) vectorization Experimental comparisons on an Alliant FX/8 show that the method results in shorter elimination trees for matrices with highly asymmetrical nonzero structure than those for previous methods that work with the symmetric structure of A+A[superscript T] or A[superscript T]A (such as George and Ng's Sparspak-C or Duff and Reid's multi-frontal method). The algorithm exploits more parallelism in the pivot search phase than previous algorithms which do not force a symmetric structure onto the matrix during any phase of the factorization. Additional experimental comparisons include fillin, amount of work, numerical stability, memory usage, and run time The nondeterministic behavior of the D2 algorithm and other performance metrics are analyzed on an Alliant FX/8, a Cray-2, and a Cray-XMP/48. Enhancements to PSolve, a pairwise pivoting algorithm, are discussed, and a software tool for developing sparse matrix algorithms and observing their dynamic behavior on a Sun workstation is presented. The tool was instrumental in the development of the D2 algorithm. Possible extensions to the D2 algorithm are discussed, including the use of dense matrix kernels and replacing the synchronization structure in the pivot search with a software combining tree. |
| Item Description: | Zugl.: Urbana, Ill., Univ., Diss. |
| Physical Description: | IX, 140 S. |
Staff View
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| 520 | 3 | |a Abstract: "This thesis presents a parallel algorithm for the direct LU factorization of general unsymmetric sparse matrices. The algorithm, D2, is based on a new nondeterministic parallel pivot search that finds a compatible pivot set S of size m, followed by a parallel rank-m update. These two steps alternate until switching to dense matrix code or until the matrix is factored. The algorithm is based on a shared-memory MIMD model and takes advantage of both concurrency and (gather-scatter) vectorization | |
| 520 | 3 | |a Experimental comparisons on an Alliant FX/8 show that the method results in shorter elimination trees for matrices with highly asymmetrical nonzero structure than those for previous methods that work with the symmetric structure of A+A[superscript T] or A[superscript T]A (such as George and Ng's Sparspak-C or Duff and Reid's multi-frontal method). The algorithm exploits more parallelism in the pivot search phase than previous algorithms which do not force a symmetric structure onto the matrix during any phase of the factorization. Additional experimental comparisons include fillin, amount of work, numerical stability, memory usage, and run time | |
| 520 | 3 | |a The nondeterministic behavior of the D2 algorithm and other performance metrics are analyzed on an Alliant FX/8, a Cray-2, and a Cray-XMP/48. Enhancements to PSolve, a pairwise pivoting algorithm, are discussed, and a software tool for developing sparse matrix algorithms and observing their dynamic behavior on a Sun workstation is presented. The tool was instrumental in the development of the D2 algorithm. Possible extensions to the D2 algorithm are discussed, including the use of dense matrix kernels and replacing the synchronization structure in the pivot search with a software combining tree. | |
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| indexdate | 2024-07-09T17:27:18Z |
| institution | BVB |
| language | English |
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| series | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |
| series2 | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |
| spelling | Davis, Timothy A. Verfasser aut A parallel algorithm for sparse unsymmetric Lu factorization by Timothy Alden Davis Reportnr. UILU ENG 89 8012 Urbana, Ill. 1989 IX, 140 S. txt rdacontent n rdamedia nc rdacarrier Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 907 Zugl.: Urbana, Ill., Univ., Diss. Abstract: "This thesis presents a parallel algorithm for the direct LU factorization of general unsymmetric sparse matrices. The algorithm, D2, is based on a new nondeterministic parallel pivot search that finds a compatible pivot set S of size m, followed by a parallel rank-m update. These two steps alternate until switching to dense matrix code or until the matrix is factored. The algorithm is based on a shared-memory MIMD model and takes advantage of both concurrency and (gather-scatter) vectorization Experimental comparisons on an Alliant FX/8 show that the method results in shorter elimination trees for matrices with highly asymmetrical nonzero structure than those for previous methods that work with the symmetric structure of A+A[superscript T] or A[superscript T]A (such as George and Ng's Sparspak-C or Duff and Reid's multi-frontal method). The algorithm exploits more parallelism in the pivot search phase than previous algorithms which do not force a symmetric structure onto the matrix during any phase of the factorization. Additional experimental comparisons include fillin, amount of work, numerical stability, memory usage, and run time The nondeterministic behavior of the D2 algorithm and other performance metrics are analyzed on an Alliant FX/8, a Cray-2, and a Cray-XMP/48. Enhancements to PSolve, a pairwise pivoting algorithm, are discussed, and a software tool for developing sparse matrix algorithms and observing their dynamic behavior on a Sun workstation is presented. The tool was instrumental in the development of the D2 algorithm. Possible extensions to the D2 algorithm are discussed, including the use of dense matrix kernels and replacing the synchronization structure in the pivot search with a software combining tree. Factorization (Mathematics) Matrices Parallel processing (Electronic computers) (DE-588)4113937-9 Hochschulschrift gnd-content Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 907 (DE-604)BV008930033 907 |
| spellingShingle | Davis, Timothy A. A parallel algorithm for sparse unsymmetric Lu factorization Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report Factorization (Mathematics) Matrices Parallel processing (Electronic computers) |
| subject_GND | (DE-588)4113937-9 |
| title | A parallel algorithm for sparse unsymmetric Lu factorization |
| title_alt | Reportnr. UILU ENG 89 8012 |
| title_auth | A parallel algorithm for sparse unsymmetric Lu factorization |
| title_exact_search | A parallel algorithm for sparse unsymmetric Lu factorization |
| title_full | A parallel algorithm for sparse unsymmetric Lu factorization by Timothy Alden Davis |
| title_fullStr | A parallel algorithm for sparse unsymmetric Lu factorization by Timothy Alden Davis |
| title_full_unstemmed | A parallel algorithm for sparse unsymmetric Lu factorization by Timothy Alden Davis |
| title_short | A parallel algorithm for sparse unsymmetric Lu factorization |
| title_sort | a parallel algorithm for sparse unsymmetric lu factorization |
| topic | Factorization (Mathematics) Matrices Parallel processing (Electronic computers) |
| topic_facet | Factorization (Mathematics) Matrices Parallel processing (Electronic computers) Hochschulschrift |
| volume_link | (DE-604)BV008930033 |
| work_keys_str_mv | AT davistimothya aparallelalgorithmforsparseunsymmetriclufactorization AT davistimothya reportnruilueng898012 |