Hyperbolic householder algorithms for factoring structured matrices:
Abstract: "We derive efficient algorithms for computing triangular decompositions of Hermitian matrices with small displacement rank using hyperbolic Householder matrices. These algorithms can be both vectorized and parallelized. Implementations along with performance results on an Alliant FX/8...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Urbana, Ill.
1989
|
| Series: | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report
877 |
| Subjects: | |
| Summary: | Abstract: "We derive efficient algorithms for computing triangular decompositions of Hermitian matrices with small displacement rank using hyperbolic Householder matrices. These algorithms can be both vectorized and parallelized. Implementations along with performance results on an Alliant FX/80, Cray X-MP/48, and Cray 2 are discussed. The use of Householder type transformations is shown to improve performance for problems with nontrivial displacement ranks. The general algorithm reduces to, in special cases, the well known Schur algorithm for factoring Toeplitz matrices and Elden's algorithm for efficient solution of least squares problems arising in the regularization of some ill-posed integral equations It gives a Householder formulation to the class of algorithms based on hyperbolic rotations studied by Kailath, Lev-Ari, Chun and their colleagues for Hermitian matrices with small displacement structure. |
| Physical Description: | 29 S. |
Staff View
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| 245 | 1 | 0 | |a Hyperbolic householder algorithms for factoring structured matrices |c George Cybenko and Michael Berry |
| 264 | 1 | |a Urbana, Ill. |c 1989 | |
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| 520 | 3 | |a Abstract: "We derive efficient algorithms for computing triangular decompositions of Hermitian matrices with small displacement rank using hyperbolic Householder matrices. These algorithms can be both vectorized and parallelized. Implementations along with performance results on an Alliant FX/80, Cray X-MP/48, and Cray 2 are discussed. The use of Householder type transformations is shown to improve performance for problems with nontrivial displacement ranks. The general algorithm reduces to, in special cases, the well known Schur algorithm for factoring Toeplitz matrices and Elden's algorithm for efficient solution of least squares problems arising in the regularization of some ill-posed integral equations | |
| 520 | 3 | |a It gives a Householder formulation to the class of algorithms based on hyperbolic rotations studied by Kailath, Lev-Ari, Chun and their colleagues for Hermitian matrices with small displacement structure. | |
| 650 | 4 | |a Toeplitz matrices | |
| 700 | 1 | |a Berry, Michael |e Verfasser |4 aut | |
| 830 | 0 | |a Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |v 877 |w (DE-604)BV008930033 |9 877 | |
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| id | DE-604.BV009258332 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:34:01Z |
| institution | BVB |
| language | English |
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| publishDate | 1989 |
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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 | Cybenko, George Verfasser aut Hyperbolic householder algorithms for factoring structured matrices George Cybenko and Michael Berry Urbana, Ill. 1989 29 S. txt rdacontent n rdamedia nc rdacarrier Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 877 Abstract: "We derive efficient algorithms for computing triangular decompositions of Hermitian matrices with small displacement rank using hyperbolic Householder matrices. These algorithms can be both vectorized and parallelized. Implementations along with performance results on an Alliant FX/80, Cray X-MP/48, and Cray 2 are discussed. The use of Householder type transformations is shown to improve performance for problems with nontrivial displacement ranks. The general algorithm reduces to, in special cases, the well known Schur algorithm for factoring Toeplitz matrices and Elden's algorithm for efficient solution of least squares problems arising in the regularization of some ill-posed integral equations It gives a Householder formulation to the class of algorithms based on hyperbolic rotations studied by Kailath, Lev-Ari, Chun and their colleagues for Hermitian matrices with small displacement structure. Toeplitz matrices Berry, Michael Verfasser aut Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 877 (DE-604)BV008930033 877 |
| spellingShingle | Cybenko, George Berry, Michael Hyperbolic householder algorithms for factoring structured matrices Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report Toeplitz matrices |
| title | Hyperbolic householder algorithms for factoring structured matrices |
| title_auth | Hyperbolic householder algorithms for factoring structured matrices |
| title_exact_search | Hyperbolic householder algorithms for factoring structured matrices |
| title_full | Hyperbolic householder algorithms for factoring structured matrices George Cybenko and Michael Berry |
| title_fullStr | Hyperbolic householder algorithms for factoring structured matrices George Cybenko and Michael Berry |
| title_full_unstemmed | Hyperbolic householder algorithms for factoring structured matrices George Cybenko and Michael Berry |
| title_short | Hyperbolic householder algorithms for factoring structured matrices |
| title_sort | hyperbolic householder algorithms for factoring structured matrices |
| topic | Toeplitz matrices |
| topic_facet | Toeplitz matrices |
| volume_link | (DE-604)BV008930033 |
| work_keys_str_mv | AT cybenkogeorge hyperbolichouseholderalgorithmsforfactoringstructuredmatrices AT berrymichael hyperbolichouseholderalgorithmsforfactoringstructuredmatrices |