The impact of parallel architectures on the solution of Eigenvalue problems:
The most significant impact on research in Scientific Computation, and Numerical Linear Algebra in particular, seems to have been brought about by the advent of vector and parallel computation. This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Haven, Connecticut
1985
|
| Series: | Yale University <New Haven, Conn.> / Department of Computer Science: Research report
444 |
| Subjects: | |
| Summary: | The most significant impact on research in Scientific Computation, and Numerical Linear Algebra in particular, seems to have been brought about by the advent of vector and parallel computation. This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. A simple model will be given to analyse the complexity of parallel algorithms on several representative multiprocessor systems: a linear processor array (or ring), a two-dimensional processor grid and the hypercube. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on the above architectures will be described, as well as parallel implementations of the following classes of eigenvalue methods: QR, bisection, divide-and-conquer, and Lanczos algorithm. |
| Physical Description: | 13 S. |
Staff View
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| 490 | 1 | |a Yale University <New Haven, Conn.> / Department of Computer Science: Research report |v 444 | |
| 520 | 3 | |a The most significant impact on research in Scientific Computation, and Numerical Linear Algebra in particular, seems to have been brought about by the advent of vector and parallel computation. This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. A simple model will be given to analyse the complexity of parallel algorithms on several representative multiprocessor systems: a linear processor array (or ring), a two-dimensional processor grid and the hypercube. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on the above architectures will be described, as well as parallel implementations of the following classes of eigenvalue methods: QR, bisection, divide-and-conquer, and Lanczos algorithm. | |
| 650 | 7 | |a Algorithms |2 dtict | |
| 650 | 7 | |a Architecture |2 dtict | |
| 650 | 7 | |a Arrays |2 dtict | |
| 650 | 7 | |a Computations |2 dtict | |
| 650 | 7 | |a Coupling(interaction) |2 dtict | |
| 650 | 7 | |a Eigenvalues |2 dtict | |
| 650 | 7 | |a Grids |2 dtict | |
| 650 | 7 | |a Impact |2 dtict | |
| 650 | 7 | |a Linear algebra |2 dtict | |
| 650 | 7 | |a Linear systems |2 dtict | |
| 650 | 7 | |a Models |2 dtict | |
| 650 | 7 | |a Multiprocessors |2 dtict | |
| 650 | 7 | |a Numerical analysis |2 dtict | |
| 650 | 7 | |a Parallel orientation |2 dtict | |
| 650 | 7 | |a Parallel processing |2 dtict | |
| 650 | 7 | |a Processing equipment |2 dtict | |
| 650 | 7 | |a Solutions(general) |2 dtict | |
| 650 | 7 | |a Surveys |2 dtict | |
| 650 | 7 | |a Symmetry |2 dtict | |
| 650 | 7 | |a Theoretical Mathematics |2 scgdst | |
| 650 | 7 | |a Two dimensional |2 dtict | |
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| 700 | 1 | |a Saad, Yousef |e Verfasser |0 (DE-588)1025729978 |4 aut | |
| 810 | 2 | |a Department of Computer Science: Research report |t Yale University <New Haven, Conn.> |v 444 |w (DE-604)BV006663362 |9 444 | |
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| id | DE-604.BV035582183 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:40:57Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017637576 |
| oclc_num | 227665843 |
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| physical | 13 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| record_format | marc |
| series2 | Yale University <New Haven, Conn.> / Department of Computer Science: Research report |
| spelling | Ipsen, Ilse C. F. Verfasser (DE-588)137389973 aut The impact of parallel architectures on the solution of Eigenvalue problems New Haven, Connecticut 1985 13 S. txt rdacontent n rdamedia nc rdacarrier Yale University <New Haven, Conn.> / Department of Computer Science: Research report 444 The most significant impact on research in Scientific Computation, and Numerical Linear Algebra in particular, seems to have been brought about by the advent of vector and parallel computation. This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. A simple model will be given to analyse the complexity of parallel algorithms on several representative multiprocessor systems: a linear processor array (or ring), a two-dimensional processor grid and the hypercube. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on the above architectures will be described, as well as parallel implementations of the following classes of eigenvalue methods: QR, bisection, divide-and-conquer, and Lanczos algorithm. Algorithms dtict Architecture dtict Arrays dtict Computations dtict Coupling(interaction) dtict Eigenvalues dtict Grids dtict Impact dtict Linear algebra dtict Linear systems dtict Models dtict Multiprocessors dtict Numerical analysis dtict Parallel orientation dtict Parallel processing dtict Processing equipment dtict Solutions(general) dtict Surveys dtict Symmetry dtict Theoretical Mathematics scgdst Two dimensional dtict Vector analysis dtict Architektur Saad, Yousef Verfasser (DE-588)1025729978 aut Department of Computer Science: Research report Yale University <New Haven, Conn.> 444 (DE-604)BV006663362 444 |
| spellingShingle | Ipsen, Ilse C. F. Saad, Yousef The impact of parallel architectures on the solution of Eigenvalue problems Algorithms dtict Architecture dtict Arrays dtict Computations dtict Coupling(interaction) dtict Eigenvalues dtict Grids dtict Impact dtict Linear algebra dtict Linear systems dtict Models dtict Multiprocessors dtict Numerical analysis dtict Parallel orientation dtict Parallel processing dtict Processing equipment dtict Solutions(general) dtict Surveys dtict Symmetry dtict Theoretical Mathematics scgdst Two dimensional dtict Vector analysis dtict Architektur |
| title | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_auth | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_exact_search | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_full | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_fullStr | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_full_unstemmed | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_short | The impact of parallel architectures on the solution of Eigenvalue problems |
| title_sort | the impact of parallel architectures on the solution of eigenvalue problems |
| topic | Algorithms dtict Architecture dtict Arrays dtict Computations dtict Coupling(interaction) dtict Eigenvalues dtict Grids dtict Impact dtict Linear algebra dtict Linear systems dtict Models dtict Multiprocessors dtict Numerical analysis dtict Parallel orientation dtict Parallel processing dtict Processing equipment dtict Solutions(general) dtict Surveys dtict Symmetry dtict Theoretical Mathematics scgdst Two dimensional dtict Vector analysis dtict Architektur |
| topic_facet | Algorithms Architecture Arrays Computations Coupling(interaction) Eigenvalues Grids Impact Linear algebra Linear systems Models Multiprocessors Numerical analysis Parallel orientation Parallel processing Processing equipment Solutions(general) Surveys Symmetry Theoretical Mathematics Two dimensional Vector analysis Architektur |
| volume_link | (DE-604)BV006663362 |
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