An evaluation of left-looking, right-looking, and multifrontal approaches to sparse Cholesky factorization hierarchical-memory machines:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Stanford, Calif.
1991
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| Schriftenreihe: | Stanford University / Computer Science Department: Report STAN-CS
1377 |
| Schlagwörter: | |
| Abstract: | 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. |
| Umfang: | 47 S. |
Internformat
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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 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-005930206 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0111 2001 B 6115-1377 |
|---|---|
| DE-BY-TUM_katkey | 1691549 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010282725 |
| _version_ | 1821933667040100354 |
| any_adam_object | |
| author | Rothberg, Edward Gupta, Anoop |
| author_facet | Rothberg, Edward Gupta, Anoop |
| author_role | aut aut |
| author_sort | Rothberg, Edward |
| author_variant | e r er a g ag |
| building | Verbundindex |
| bvnumber | BV008979500 |
| ctrlnum | (OCoLC)24995553 (DE-599)BVBBV008979500 |
| format | Book |
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| id | DE-604.BV008979500 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:29:50Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005930206 |
| oclc_num | 24995553 |
| open_access_boolean | |
| owner | DE-29T DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-91G DE-BY-TUM |
| physical | 47 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | Stanford University / Computer Science Department: Report STAN-CS |
| 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 |
| work_keys_str_mv | AT rothbergedward anevaluationofleftlookingrightlookingandmultifrontalapproachestosparsecholeskyfactorizationhierarchicalmemorymachines AT guptaanoop anevaluationofleftlookingrightlookingandmultifrontalapproachestosparsecholeskyfactorizationhierarchicalmemorymachines AT rothbergedward reportnrcsltr91487 AT guptaanoop reportnrcsltr91487 |
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik, Berichte
| Signatur: |
0111 2001 B 6115-1377
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |