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Browsing by Author "Brent, Richard P."
Now showing items 19 of 9

Computation of the Singular Value Decomposition Using MeshConnected Processors
Brent, Richard P.; Luk, Franklin T.; Van Loan, Charles (Cornell University, 198203)A cyclic Jacobi method for computing the singular value decomposition of an $mxn$ matrix $(m \geq n)$ using systolic arrays is proposed. The algorithm requires $O(n^{2})$ processors and $O(m + n \log n)$ units of time. 
Computing the Cholesky Factorization Using a Systolic Architecture
Brent, Richard P.; Luk, Franklin T. (Cornell University, 198209)This note concerns the computation of the Cholesky factorization of a symmetric and positive definite matrix on a systolic array. We use the special properties of the matrix to simplify the algorithm and the corresponding ... 
omputation of the Generalized Singular Value Decomposition Using MeshConnected Processors
Brent, Richard P.; Luk, Franklin T.; Van Loan, Charles (Cornell University, 198307)This paper concerns the systolic array computation of the generalized singular value decomposition. Numerical algorithms for both one and twodimensional systolic architectures are discussed. 
The Solution of Singular Value Problems Using Systolic Arrays
Brent, Richard P.; Luk, Franklin T. (Cornell University, 198408)This paper contains the computation of the singular value decomposition using systolic arrays. Two different linear time algorithms are presented. 
The Solution of SingularValue and Symmetric Eigenvalue Problems on Multiprocessor Arrays
Brent, Richard P.; Luk, Franklin T. (Cornell University, 198307)Parallel Jacobilike algorithms are presented for computing a singularvalue 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 ... 
Some LinearTime Algorithms for Systolic Arrays
Brent, Richard P.; Kung, H. T.; Luk, Franklin T. (Cornell University, 198301)We survey some recent results on lineartime and almost lineartime algorithms for one and twodimensional systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree $n$ ... 
A Systolic Architecture for Almost LinearTime Solution of the Symmetric Eigenvalue Problem
Brent, Richard P.; Luk, Franklin T. (Cornell University, 198208)An algorithm is presented for computing the eigenvalues and eigenvectors of an n x n real symmetric matrix. The algorithm is essentially a Jacobi method implemented on a twodimensional systolic array of $O(n^{2})$ ... 
A Systolic Architecture for the Singular Value Decomposition
Brent, Richard P.; Luk, Franklin T. (Cornell University, 198209)We propose a systolic architecture for computing a singular value decomposition of an m x n matrix, where $m \geq n$. Our algorithm is stable and requires only $O(mn)$ time on a linear array of $O(n)$ processors. ... 
A Systolic Array for the LinearTime Solution of Toeplitz Systems of Equations
Brent, Richard P.; Luk, Franklin T. (Cornell University, 198211)The solution of an (n+1)x(n+1) Toeplitz system of linear equations on a onedimensional systolic architecture is studied. Our implementation of an algorithm due to Bareiss is shown to require only $O(n)$ time and $O(n)$ ...