Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals:
It is shown in this paper that certain orthogonal polynomials over two disjoint intervals can be particularly useful for solving large symmetric indefinite linear systems or for finding a few interior eigenvalues of a large symmetric matrix. There are several advantages of the proposed approach over...
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
[New Haven, Conn.]
1981
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| Series: | Yale University <New Haven, Conn.> / Department of Computer Science: Research report
212 |
| Subjects: | |
| Summary: | It is shown in this paper that certain orthogonal polynomials over two disjoint intervals can be particularly useful for solving large symmetric indefinite linear systems or for finding a few interior eigenvalues of a large symmetric matrix. There are several advantages of the proposed approach over the techniques which are based upon the polynomials having the least uniform norm in two intervals. While a theoretical comparison will show that the norms of the minimal polynomial of degree n in the least squares sense differs from the minimax polynomial of the same degree by a factor not exceeding 2(n+1)to the 0.5 power, the least squares polynomials are by far easier to compute and to use thanks to their three term recurrence relation. A number of suggestions will be made for the problem of estimating the optimal parameters and several numerical experiments will be reported. (Author). |
| Physical Description: | 51 Bl. |
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| 245 | 1 | 0 | |a Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
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| 490 | 1 | |a Yale University <New Haven, Conn.> / Department of Computer Science: Research report |v 212 | |
| 520 | 3 | |a It is shown in this paper that certain orthogonal polynomials over two disjoint intervals can be particularly useful for solving large symmetric indefinite linear systems or for finding a few interior eigenvalues of a large symmetric matrix. There are several advantages of the proposed approach over the techniques which are based upon the polynomials having the least uniform norm in two intervals. While a theoretical comparison will show that the norms of the minimal polynomial of degree n in the least squares sense differs from the minimax polynomial of the same degree by a factor not exceeding 2(n+1)to the 0.5 power, the least squares polynomials are by far easier to compute and to use thanks to their three term recurrence relation. A number of suggestions will be made for the problem of estimating the optimal parameters and several numerical experiments will be reported. (Author). | |
| 650 | 4 | |a Orthogonal polynomials | |
| 650 | 7 | |a Chebyshev polynomials |2 dtict | |
| 650 | 7 | |a Eigenvalues |2 dtict | |
| 650 | 7 | |a Iterations |2 dtict | |
| 650 | 7 | |a Least squares method |2 dtict | |
| 650 | 7 | |a Linear systems |2 dtict | |
| 650 | 7 | |a Orthogonality |2 dtict | |
| 650 | 7 | |a Polynomials |2 dtict | |
| 650 | 7 | |a Statistics and Probability |2 scgdst | |
| 810 | 2 | |a Department of Computer Science: Research report |t Yale University <New Haven, Conn.> |v 212 |w (DE-604)BV006663362 |9 212 | |
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Record in the Search Index
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| id | DE-604.BV010028435 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:45:13Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006650102 |
| oclc_num | 227535686 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 51 Bl. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| record_format | marc |
| series2 | Yale University <New Haven, Conn.> / Department of Computer Science: Research report |
| spelling | Saad, Yousef Verfasser (DE-588)1025729978 aut Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals [New Haven, Conn.] 1981 51 Bl. txt rdacontent n rdamedia nc rdacarrier Yale University <New Haven, Conn.> / Department of Computer Science: Research report 212 It is shown in this paper that certain orthogonal polynomials over two disjoint intervals can be particularly useful for solving large symmetric indefinite linear systems or for finding a few interior eigenvalues of a large symmetric matrix. There are several advantages of the proposed approach over the techniques which are based upon the polynomials having the least uniform norm in two intervals. While a theoretical comparison will show that the norms of the minimal polynomial of degree n in the least squares sense differs from the minimax polynomial of the same degree by a factor not exceeding 2(n+1)to the 0.5 power, the least squares polynomials are by far easier to compute and to use thanks to their three term recurrence relation. A number of suggestions will be made for the problem of estimating the optimal parameters and several numerical experiments will be reported. (Author). Orthogonal polynomials Chebyshev polynomials dtict Eigenvalues dtict Iterations dtict Least squares method dtict Linear systems dtict Orthogonality dtict Polynomials dtict Statistics and Probability scgdst Department of Computer Science: Research report Yale University <New Haven, Conn.> 212 (DE-604)BV006663362 212 |
| spellingShingle | Saad, Yousef Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals Orthogonal polynomials Chebyshev polynomials dtict Eigenvalues dtict Iterations dtict Least squares method dtict Linear systems dtict Orthogonality dtict Polynomials dtict Statistics and Probability scgdst |
| title | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_auth | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_exact_search | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_full | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_fullStr | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_full_unstemmed | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_short | Iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| title_sort | iterative solution of indefinite symmetric systems by methods using orthogonal polynomials over two disjoint intervals |
| topic | Orthogonal polynomials Chebyshev polynomials dtict Eigenvalues dtict Iterations dtict Least squares method dtict Linear systems dtict Orthogonality dtict Polynomials dtict Statistics and Probability scgdst |
| topic_facet | Orthogonal polynomials Chebyshev polynomials Eigenvalues Iterations Least squares method Linear systems Orthogonality Polynomials Statistics and Probability |
| volume_link | (DE-604)BV006663362 |
| work_keys_str_mv | AT saadyousef iterativesolutionofindefinitesymmetricsystemsbymethodsusingorthogonalpolynomialsovertwodisjointintervals |