Now showing items 1-19 of 19

    • The Communality Problem for Stieltjes Matrices 

      Luk, Franklin T. (Cornell University, 1980-04)
      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 Mesh-Connected Processors 

      Brent, Richard P.; Luk, Franklin T.; Van Loan, Charles (Cornell University, 1982-03)
      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, 1982-09)
      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, 1980-04)
      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 Golub-Reinsch algorithm is not ...
    • Engineering: Cornell Quarterly, Vol.23, No.1 (Autumn 1988): A New Thrust in Electronics Research 

      Shealy, J. Richard; Krusius, J. Peter; Al-Omar, Abdul-Azeez; Weinzierl, Steven R.; Luk, Franklin T.; Schimmel, David E.; Torng, H. C.; Tang, C. L.; Bilardi, Gianfranco; Pollock, Clifford R. (Internet-First 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 High-Speed 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, 1980-09)
      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 Jacobi-like Algorithm for Computing the QR-Decomposition 

      Luk, Franklin T. (Cornell University, 1984-05)
      A parallel Jacobi-like method for computing the QR-decomposition 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, 1982-01)
      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 Mesh-Connected Processors 

      Brent, Richard P.; Luk, Franklin T.; Van Loan, Charles (Cornell University, 1983-07)
      This paper concerns the systolic array computation of the generalized singular value decomposition. Numerical algorithms for both one and two-dimensional systolic architectures are discussed.
    • On the Minres Method of Factor Analysis 

      Luk, Franklin T. (Cornell University, 1981-08)
      The minres method is an effective means for estimating factor loadings under the condition that the sum of squares of the off-diagonal residuals be minimized. This paper is addressed to the efficient implementation and ...
    • Orthogonal Rotation to a Partially Specified Target 

      Luk, Franklin T. (Cornell University, 1981-09)
      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 M-Matrices 

      Luk, Franklin T.; Pagano, Marcello (Cornell University, 1979-10)
      In this paper, we study the problem of quadratic programming with M-matrices. 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, 1984-08)
      This paper contains the computation of the singular value decomposition using systolic arrays. Two different linear time algorithms are presented.
    • The Solution of Singular-Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays 

      Brent, Richard P.; Luk, Franklin T. (Cornell University, 1983-07)
      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 ...
    • Some Linear-Time Algorithms for Systolic Arrays 

      Brent, Richard P.; Kung, H. T.; Luk, Franklin T. (Cornell University, 1983-01)
      We survey some recent results on linear-time and almost linear-time algorithms for one and two-dimensional systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree $n$ ...
    • A Systolic Architecture for Almost Linear-Time Solution of the Symmetric Eigenvalue Problem 

      Brent, Richard P.; Luk, Franklin T. (Cornell University, 1982-08)
      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 two-dimensional systolic array of $O(n^{2})$ ...
    • A Systolic Architecture for the Singular Value Decomposition 

      Brent, Richard P.; Luk, Franklin T. (Cornell University, 1982-09)
      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 Linear-Time Solution of Toeplitz Systems of Equations 

      Brent, Richard P.; Luk, Franklin T. (Cornell University, 1982-11)
      The solution of an (n+1)x(n+1) Toeplitz system of linear equations on a one-dimensional 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, 1984-07)
      A triangular processor array for computing a singular value decomposition (SVD) of an $m \times n (m \geq n)$ matrix is proposed. A Jacobi-type algorithm is used to first triangularize the given matrix and then diagonalize ...