Solving general sparse linear systems using conjugate gradient-type methods:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Urbana, Ill.
1989
|
| Schriftenreihe: | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report
895 |
| Schlagwörter: | |
| Abstract: | Abstract: "The problem of finding an approximation of x=A[superscript [symbol]]b (where A[superscript [symbol]] is the pseudo-inverse of A [is an element of] R[superscript mxn] with m [is greater than or equal to] n and rank(A)=n) is discussed. It is assumed that A is sparse but has neither a special pattern (as bandedness) nor a special property (as symmetry or positive definiteness). In this paper it is shown that preconditioners obtained by neglecting small elements during the decomposition of A into easily invertible matrices could efficiently be used with gradient-type methods. The preconditioned methods so found are often better than the corresponding direct and pure iterative method Preconditionings in which elements are neglected not because they are small but because they appear at inconvenient places may fail in cases where those obtained by neglecting only small elements succeed (provided that an adaptive strategy for deciding when an element is small is implemented). Numerical results are given to illustrate the performance of preconditioning based on neglecting small elements in connection with conjugate gradient-type methods. |
| Umfang: | 11 S. |
Internformat
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| 100 | 1 | |a Sameh, Ahmed |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Solving general sparse linear systems using conjugate gradient-type methods |c Ahmed Sameh and Zahari Zlatev |
| 264 | 1 | |a Urbana, Ill. |c 1989 | |
| 300 | |a 11 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |v 895 | |
| 520 | 3 | |a Abstract: "The problem of finding an approximation of x=A[superscript [symbol]]b (where A[superscript [symbol]] is the pseudo-inverse of A [is an element of] R[superscript mxn] with m [is greater than or equal to] n and rank(A)=n) is discussed. It is assumed that A is sparse but has neither a special pattern (as bandedness) nor a special property (as symmetry or positive definiteness). In this paper it is shown that preconditioners obtained by neglecting small elements during the decomposition of A into easily invertible matrices could efficiently be used with gradient-type methods. The preconditioned methods so found are often better than the corresponding direct and pure iterative method | |
| 520 | 3 | |a Preconditionings in which elements are neglected not because they are small but because they appear at inconvenient places may fail in cases where those obtained by neglecting only small elements succeed (provided that an adaptive strategy for deciding when an element is small is implemented). Numerical results are given to illustrate the performance of preconditioning based on neglecting small elements in connection with conjugate gradient-type methods. | |
| 650 | 4 | |a Linear systems | |
| 650 | 4 | |a Sparse matrices |x Computer programs | |
| 700 | 1 | |a Zlatev, Zahari |d 1939- |e Verfasser |0 (DE-588)13264357X |4 aut | |
| 830 | 0 | |a Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |v 895 |w (DE-604)BV008930033 |9 895 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006160384 | |
Datensatz im Suchindex
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| author | Sameh, Ahmed Zlatev, Zahari 1939- |
| author_GND | (DE-588)13264357X |
| author_facet | Sameh, Ahmed Zlatev, Zahari 1939- |
| author_role | aut aut |
| author_sort | Sameh, Ahmed |
| author_variant | a s as z z zz |
| building | Verbundindex |
| bvnumber | BV009258328 |
| ctrlnum | (OCoLC)21429748 (DE-599)BVBBV009258328 |
| format | Book |
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| id | DE-604.BV009258328 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:35:12Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006160384 |
| oclc_num | 21429748 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | 11 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| record_format | marc |
| series | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |
| series2 | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |
| spelling | Sameh, Ahmed Verfasser aut Solving general sparse linear systems using conjugate gradient-type methods Ahmed Sameh and Zahari Zlatev Urbana, Ill. 1989 11 S. txt rdacontent n rdamedia nc rdacarrier Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 895 Abstract: "The problem of finding an approximation of x=A[superscript [symbol]]b (where A[superscript [symbol]] is the pseudo-inverse of A [is an element of] R[superscript mxn] with m [is greater than or equal to] n and rank(A)=n) is discussed. It is assumed that A is sparse but has neither a special pattern (as bandedness) nor a special property (as symmetry or positive definiteness). In this paper it is shown that preconditioners obtained by neglecting small elements during the decomposition of A into easily invertible matrices could efficiently be used with gradient-type methods. The preconditioned methods so found are often better than the corresponding direct and pure iterative method Preconditionings in which elements are neglected not because they are small but because they appear at inconvenient places may fail in cases where those obtained by neglecting only small elements succeed (provided that an adaptive strategy for deciding when an element is small is implemented). Numerical results are given to illustrate the performance of preconditioning based on neglecting small elements in connection with conjugate gradient-type methods. Linear systems Sparse matrices Computer programs Zlatev, Zahari 1939- Verfasser (DE-588)13264357X aut Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 895 (DE-604)BV008930033 895 |
| spellingShingle | Sameh, Ahmed Zlatev, Zahari 1939- Solving general sparse linear systems using conjugate gradient-type methods Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report Linear systems Sparse matrices Computer programs |
| title | Solving general sparse linear systems using conjugate gradient-type methods |
| title_auth | Solving general sparse linear systems using conjugate gradient-type methods |
| title_exact_search | Solving general sparse linear systems using conjugate gradient-type methods |
| title_full | Solving general sparse linear systems using conjugate gradient-type methods Ahmed Sameh and Zahari Zlatev |
| title_fullStr | Solving general sparse linear systems using conjugate gradient-type methods Ahmed Sameh and Zahari Zlatev |
| title_full_unstemmed | Solving general sparse linear systems using conjugate gradient-type methods Ahmed Sameh and Zahari Zlatev |
| title_short | Solving general sparse linear systems using conjugate gradient-type methods |
| title_sort | solving general sparse linear systems using conjugate gradient type methods |
| topic | Linear systems Sparse matrices Computer programs |
| topic_facet | Linear systems Sparse matrices Computer programs |
| volume_link | (DE-604)BV008930033 |
| work_keys_str_mv | AT samehahmed solvinggeneralsparselinearsystemsusingconjugategradienttypemethods AT zlatevzahari solvinggeneralsparselinearsystemsusingconjugategradienttypemethods |