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# The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays

Author: R P Brent; Franklin T Luk; Mathematical Sciences Research Centre.; Australian National University. Centre for Mathematical Analysis.; Cornell University. Department of Computer Science. Ithaca, NY : Cornell University, 1983. Book : EnglishView all editions and formats WorldCat Parallel Jacobi-like algorithms are presented for computing a singular-value decomposition of an $mxn$ matrix $(m \geq n)$ and an eigenvalue decomposition of an $n x n$ symmetric matrix. A linear array of $O(n)$ processors is proposed for the singular-value problem and the associated algorithm requires time $O(mnS)$, where $S$ is the number of sweeps (typically $S \leq 10)$. A square array of $O(n[superscript]{2})$ processors with nearest-neighbor communication is proposed for the eigenvalue problem; the associated algorithm requires time $O(nS)$.Key Words And Phrases: Multiprocessor arrays, systolic arrays, singular-value decomposition, eigenvalue decomposition, real symmetric matrices, Hestenes method, Jacobi method, VLSI, real-time computation, parallel algorithms.  Read more... (not yet rated) 0 with reviews - Be the first.

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Document Type: Book R P Brent; Franklin T Luk; Mathematical Sciences Research Centre.; Australian National University. Centre for Mathematical Analysis.; Cornell University. Department of Computer Science. Find more information about: R P Brent Franklin T Luk 10649105 "TR 83-562.""July 1983." 34 pages ; 28 cm R.P. Brent, F.T. Luk.

### Abstract:

Parallel Jacobi-like algorithms are presented for computing a singular-value decomposition of an $mxn$ matrix $(m \geq n)$ and an eigenvalue decomposition of an $n x n$ symmetric matrix. A linear array of $O(n)$ processors is proposed for the singular-value problem and the associated algorithm requires time $O(mnS)$, where $S$ is the number of sweeps (typically $S \leq 10)$. A square array of $O(n[superscript]{2})$ processors with nearest-neighbor communication is proposed for the eigenvalue problem; the associated algorithm requires time $O(nS)$.

Key Words And Phrases: Multiprocessor arrays, systolic arrays, singular-value decomposition, eigenvalue decomposition, real symmetric matrices, Hestenes method, Jacobi method, VLSI, real-time computation, parallel algorithms.

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