JavaScript is disabled for your browser. Some features of this site may not work without it.
Browsing by Author "Luk, Franklin T."
Now showing items 119 of 19

The Communality Problem for Stieltjes Matrices
Luk, Franklin T. (Cornell University, 198004)The Communality Problem in Factor Analysis is that of reducing the diagonal elements of a correlation matrix so that the resulting matrix will be positive semidefinite and of minimum rank. The problem is well studied but ... 
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 ... 
Computing the Singular Value Decomposition on the Illiac IV
Luk, Franklin T. (Cornell University, 198004)In this paper, we study the computation of the singular value decomposition of a matrix on the ILLIAC IV computer. We describe the architecture of the machine and explain why the standard GolubReinsch algorithm is not ... 
Engineering: Cornell Quarterly, Vol.23, No.1 (Autumn 1988): A New Thrust in Electronics Research
Shealy, J. Richard; Krusius, J. Peter; AlOmar, AbdulAzeez; Weinzierl, Steven R.; Luk, Franklin T.; Schimmel, David E.; Torng, H. C.; Tang, C. L.; Bilardi, Gianfranco; Pollock, Clifford R. (InternetFirst University Press, 1988)IN THIS ISSUE: Cornell and JSEP: A New Thrust in a Major Program of Electronics Research /2 ... Growing Crystalline Layers for New HighSpeed Electron Devices /4 J. Richard Shealy ... Supercomputer Simulation for Understanding ... 
A Generalized Broyden's Method for Solving Simultaneous Linear Equations
Gerber, Richard R.; Luk, Franklin T. (Cornell University, 198009)We present a generalized Broyden's method for solving rectangular systems of linear equations. We show that the method computes a least squares solution to the given simultaneous equations and that it posseses a remarkable ... 
A Jacobilike Algorithm for Computing the QRDecomposition
Luk, Franklin T. (Cornell University, 198405)A parallel Jacobilike method for computing the QRdecomposition of an $n \times n$ matrix is proposed. It requires $O(n^{2})$ processors and $O(n)$ units of time. The method can be extended to handle an $m \times n$ ... 
Oblique Procrustes Rotations in Factor Analysis
Luk, Franklin T. (Cornell University, 198201)This paper addresses the problem of rotating a factor matrix obliquely to a least squares fit to a target matrix. The target may be fully or partially specified. An iterative computing procedure is presented. Keywords: ... 
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. 
On the Minres Method of Factor Analysis
Luk, Franklin T. (Cornell University, 198108)The minres method is an effective means for estimating factor loadings under the condition that the sum of squares of the offdiagonal residuals be minimized. This paper is addressed to the efficient implementation and ... 
Orthogonal Rotation to a Partially Specified Target
Luk, Franklin T. (Cornell University, 198109)This paper addresses the problem of finding an orthogonal transformation of an arbitrary factor solution that would lead to a least squares fit of a partially specified target matrix. An iterative computing procedure is ... 
Quadratic Programming with MMatrices
Luk, Franklin T.; Pagano, Marcello (Cornell University, 197910)In this paper, we study the problem of quadratic programming with Mmatrices. We describe (1) an effective algorithm for the case where the variables are subject to a lower bound constraint, and (2) an analogous algorithm ... 
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 $O(n)$ ... 
A Triangular Processor Array for Computing the Singular Value Decomposition
Luk, Franklin T. (Cornell University, 198407)A triangular processor array for computing a singular value decomposition (SVD) of an $m \times n (m \geq n)$ matrix is proposed. A Jacobitype algorithm is used to first triangularize the given matrix and then diagonalize ...