An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines:
Abstract: "In this paper we present a comprehensive analysis of the performance of a variety of sparse Cholesky factorization methods on hierarchical-memory machines. We investigate methods that vary along two different axes. Along the first axis, we consider three different high- level approac...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Stanford, Calif.
1991
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| Schriftenreihe: | Stanford University / Computer Science Department: Report STAN-CS
1377 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "In this paper we present a comprehensive analysis of the performance of a variety of sparse Cholesky factorization methods on hierarchical-memory machines. We investigate methods that vary along two different axes. Along the first axis, we consider three different high- level approaches to sparse factorization: left-looking, right-looking, and multifrontal. Along the second axis, we consider the implementation of each of these high-level approaches using different sets of primitives. The primitives vary based on the structures they manipulate. One important structure in sparse Cholesky factorization is a single column of the matrix. We first consider primitives that manipulate single columns These are the most commonly used primitives for expressing the sparse Cholesky computation. Antoher important structure is the supernode, a set of columns with identical non-zero structures. We consider sets of primitives that exploit the supernodal structure of the matrix to varying degrees. We find that primitives that manipulate larger structures greatly increase the amount of exploitable data reuse, thus leading to dramatically higher performance on hierarchical-memory machines. We observe performance increases of two to three times when comparing methods based on primitives that make extensive use of the supernodal structure to methods based on primitives that manipulate columns We also find that the overall approach (left-looking, right- looking, or multifrontal) is less important for performance than the particular set of primitives used to implement the approach. |
| Beschreibung: | 47 S. |
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| 100 | 1 | |a Rothberg, Edward |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines |c Edward Rothberg and Anoop Gupta |
| 246 | 1 | 3 | |a Reportnr.: CSL TR 91 487 |
| 264 | 1 | |a Stanford, Calif. |c 1991 | |
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| 490 | 1 | |a Stanford University / Computer Science Department: Report STAN-CS |v 1377 | |
| 520 | 3 | |a Abstract: "In this paper we present a comprehensive analysis of the performance of a variety of sparse Cholesky factorization methods on hierarchical-memory machines. We investigate methods that vary along two different axes. Along the first axis, we consider three different high- level approaches to sparse factorization: left-looking, right-looking, and multifrontal. Along the second axis, we consider the implementation of each of these high-level approaches using different sets of primitives. The primitives vary based on the structures they manipulate. One important structure in sparse Cholesky factorization is a single column of the matrix. We first consider primitives that manipulate single columns | |
| 520 | 3 | |a These are the most commonly used primitives for expressing the sparse Cholesky computation. Antoher important structure is the supernode, a set of columns with identical non-zero structures. We consider sets of primitives that exploit the supernodal structure of the matrix to varying degrees. We find that primitives that manipulate larger structures greatly increase the amount of exploitable data reuse, thus leading to dramatically higher performance on hierarchical-memory machines. We observe performance increases of two to three times when comparing methods based on primitives that make extensive use of the supernodal structure to methods based on primitives that manipulate columns | |
| 520 | 3 | |a We also find that the overall approach (left-looking, right- looking, or multifrontal) is less important for performance than the particular set of primitives used to implement the approach. | |
| 650 | 4 | |a Factorization (Mathematics) | |
| 650 | 4 | |a Matrices | |
| 700 | 1 | |a Gupta, Anoop |e Verfasser |4 aut | |
| 810 | 2 | |a Computer Science Department: Report STAN-CS |t Stanford University |v 1377 |w (DE-604)BV008928280 |9 1377 | |
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| author | Rothberg, Edward Gupta, Anoop |
| author_facet | Rothberg, Edward Gupta, Anoop |
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| id | DE-604.BV008979500 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:27:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005930206 |
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| physical | 47 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
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| series2 | Stanford University / Computer Science Department: Report STAN-CS |
| spelling | Rothberg, Edward Verfasser aut An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines Edward Rothberg and Anoop Gupta Reportnr.: CSL TR 91 487 Stanford, Calif. 1991 47 S. txt rdacontent n rdamedia nc rdacarrier Stanford University / Computer Science Department: Report STAN-CS 1377 Abstract: "In this paper we present a comprehensive analysis of the performance of a variety of sparse Cholesky factorization methods on hierarchical-memory machines. We investigate methods that vary along two different axes. Along the first axis, we consider three different high- level approaches to sparse factorization: left-looking, right-looking, and multifrontal. Along the second axis, we consider the implementation of each of these high-level approaches using different sets of primitives. The primitives vary based on the structures they manipulate. One important structure in sparse Cholesky factorization is a single column of the matrix. We first consider primitives that manipulate single columns These are the most commonly used primitives for expressing the sparse Cholesky computation. Antoher important structure is the supernode, a set of columns with identical non-zero structures. We consider sets of primitives that exploit the supernodal structure of the matrix to varying degrees. We find that primitives that manipulate larger structures greatly increase the amount of exploitable data reuse, thus leading to dramatically higher performance on hierarchical-memory machines. We observe performance increases of two to three times when comparing methods based on primitives that make extensive use of the supernodal structure to methods based on primitives that manipulate columns We also find that the overall approach (left-looking, right- looking, or multifrontal) is less important for performance than the particular set of primitives used to implement the approach. Factorization (Mathematics) Matrices Gupta, Anoop Verfasser aut Computer Science Department: Report STAN-CS Stanford University 1377 (DE-604)BV008928280 1377 |
| spellingShingle | Rothberg, Edward Gupta, Anoop An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines Factorization (Mathematics) Matrices |
| title | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines |
| title_alt | Reportnr.: CSL TR 91 487 |
| title_auth | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines |
| title_exact_search | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines |
| title_full | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines Edward Rothberg and Anoop Gupta |
| title_fullStr | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines Edward Rothberg and Anoop Gupta |
| title_full_unstemmed | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines Edward Rothberg and Anoop Gupta |
| title_short | An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines |
| title_sort | an evaluation of left looking right looking and multifrontal approaches to sparse cholesky factorization hierarchical memory machines |
| topic | Factorization (Mathematics) Matrices |
| topic_facet | Factorization (Mathematics) Matrices |
| volume_link | (DE-604)BV008928280 |
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