Systolic givens factorization of dense rectangular matrices
Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an algorithm which is executed in m+n- 2 steps on a linear array of [m/2] processors, a step being the time necessary to achieve a Givens rotation. The...
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| Published in: | International journal of computer mathematics Vol. 25; no. 3-4; pp. 287 - 298 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Abingdon
Gordon and Breach Science Publishers
01.01.1988
Taylor and Francis Taylor & Francis |
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| ISSN: | 0020-7160, 1029-0265 |
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| Abstract | Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an algorithm which is executed in m+n- 2 steps on a linear array of [m/2] processors, a step being the time necessary to achieve a Givens rotation. The pipelined version of the new algorithm leads to a systolic implementation whose area-time performances overcome those of the arrays of Bojanczyk, Brent and Kung [1] and Gentleman and Kung [5]. |
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| AbstractList | Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an algorithm which is executed in m+n- 2 steps on a linear array of [m/2] processors, a step being the time necessary to achieve a Givens rotation. The pipelined version of the new algorithm leads to a systolic implementation whose area-time performances overcome those of the arrays of Bojanczyk, Brent and Kung [1] and Gentleman and Kung [5]. |
| Author | Robert, Yves Cosnard, Michel |
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| Copyright | Copyright Taylor & Francis Group, LLC 1988 1989 INIST-CNRS Distributed under a Creative Commons Attribution 4.0 International License |
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| Keywords | Numerical analysis VLSI circuit Least squares method Parallel processing Systolic network Algorithm Factorization Implementation |
| Language | English |
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| References | Schendel U. (CIT0022) 1984 CIT0021 Leiserson C.E. (CIT0015) 1981 CIT0023 Golub G.H. (CIT0007) 1983 Hwang K. (CIT0011) 1984 Ullman J.D. (CIT0024) 1983 Lawson C. (CIT0014) 1974 Bojanczyk A. (CIT0001) 1981 Kung H.T. (CIT0012) 1982; 15 CIT0003 Sameh A. (CIT0018) 1977 CIT0002 CIT0013 CIT0005 CIT0016 CIT0004 Sameh A. (CIT0020) 1983 CIT0006 CIT0017 CIT0009 CIT0008 Horwarth S. (CIT0010) 1980 CIT0019 |
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| Snippet | Given an m by n dense matrix A(m≧n) we consider parallel algorithms to compute its orthogonal factorization via Givens rotations. First we describe an... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences B.7.1 [Integrated circuits] Computer Science Computer science; control theory; systems Distributed, Parallel, and Cluster Computing Exact sciences and technology F.2.1 [Analysis of algorithms and problem complexity] F.l.l [Computation by abstract devices] Givens rotations linear least squares problems Models fo Computation-Systolic array Numerical algorithms and problems-QR decomposition of a dense matrix QR factorization Systolic algorithms Theoretical computing Types and design styles-Algorithms implemented in hardware VLSI VLSI architectures |
| Title | Systolic givens factorization of dense rectangular matrices |
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