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Browsing by Author "Van Loan, Charles"
Now showing items 120 of 29

A HamiltonianSchur Decomposition
Paige, Chris; Van Loan, Charles (Cornell University, 197909) 
Analysis of Some Matrix Problems Using the CS Decomposition
Van Loan, Charles (Cornell University, 198403)The gist of the CS decomposition is that the blocks of a partitioned orthogonal matrix have related singular value decompositions. In this paper we develop a perturbation theory for the CS decomposition and use it to ... 
An Analysis of the Total Least Squares Problem
Golub, Gene H.; Van Loan, Charles (Cornell University, 198002)Totla least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector $b (mxl)$ and in the data matrix $A (mxn)$. The technique has been discussed by several authors ... 
The Block Jacobi Method for Computing the Singular Value Decomposition
Van Loan, Charles (Cornell University, 198506)Jacobi techniques for computing the symmetric eigenvalue and singular value decompositions have achieved recent prominence because of interest in parallel computation. They are ideally suited for certain multiprocessor ... 
A Block or Factorization Scheme for Loosely Coupled Systems of Array Processors
Van Loan, Charles (Cornell University, 198612)A statically scheduled parallel block QR factorization procedure is described. It is based on "block" Givens rotations and is modeled after the GentlemanKung systolic QR procedure. Independent tasks are associated with ... 
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. 
Computer Science and the Liberal Arts Student
Van Loan, Charles (Cornell University, 197905)The computer science education of nontechnical liberal arts students is a matter of increasing concern. In this paper it is argued that computer scientists should promote and teach their subject more in line with the ... 
Computing Integrals Involving the Matrix Exponential
Van Loan, Charles (Cornell University, 197712)A new algorithm for computing integrals involving the matrix exponential is given. The method employs diagonal Pade approximation with scaling and squaring. Rigorous truncation error bounds are given and incorporated in ... 
Computing the CS and the Generalized Singular Value Decompositions
Van Loan, Charles (Cornell University, 198406)If the columns of a matrix are orthonormal and it is partitioned into a 2by1 block matrix, then the singular value decompositions of the blocks are related. This is the essence of the "CS decomposition". The computation ... 
Computing the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix
Cybenko, George; Van Loan, Charles (Cornell University, 198204)A method for computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix is given. It relies solely upon the LevinsonDurbin algorithm. The procedure involves a combination of bisection and Newton's ... 
Generalizing the LINPACK Condition Estimator
Cline, A. K.; Conn, Andrew R.; Van Loan, Charles (Cornell University, 198106)Two generalizations of the ClineMolerStewartWilkinson "LINPACK" condition estimator are described. One generalization combines the LINPACK notion of "lookahead" with a new feature called "lookbehind" that results ... 
A HessenbergSchur Method for the Problem AX + XB = C
Golub, Gene H.; Nash, Stephen; Van Loan, Charles (Cornell University, 197810)ONe of the most effective methods for solving the matrix equation AX + XB = C is the BartelsStewart algorithm. Key to this technique is the orthogonal reduction of A and B to triangular form using the QR algorithm for ... 
How Near is a Stable Matrix to an Unstable Matrix?
Van Loan, Charles (Cornell University, 198410)In this paper we explore how close a given stable matrix A is to being unstable. As a measure of "how stable" a stable matrix is, the spectral abscissa is shown to be flawed. A better measure of stability is the Frobenius ... 
Integral Transform Estimation and Compartmental Models
Contreras, Martha; Liu, Changmei; Casella, George; Ryan, Louise M.; Van Loan, Charles; Cornell University. Biometrics Unit.; Cornell University. Dept. of Biometrics.; Cornell University. Dept. of Biological Statistics and Computational Biology. (1997) 
Lectures in Least Squares
Van Loan, Charles (Cornell University, 197605)These lecture notes arose out of the numerical analysis seminar given at Cornell University in the Spring of 1976. The goal of the seminar was to acquaint a variety of researchers and undergraduates with the field of ... 
Matrix Computations and Signal Processing
Van Loan, Charles (Cornell University, 198709)The interactions between the signal processing and matrix computation areas is explored by examining some subspace dimension estimation problems that arise in a pair of directionofarrival algorithms: MUSIC and ESPRIT. ... 
Nineteen Ways to Compute the Exponential of a Matrix
Moler, C. B.; Van Loan, Charles (Cornell University, 197607)In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. ... 
A Note on the Evaluation of Matrix Polynomials
Van Loan, Charles (Cornell University, 197809)The problem of evaluating a polynomial p(x) in a matrix A arises in many applications, e.g. the Taylor approximation of $e^{A}$. The $O(\sqrt{q}n^{3})$ algorithm of Paterson and Stockmeyer has the drawback that it requires ... 
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 Computing the CS Decomposition with Systolic Arrays
Kaplan, I. M.; Van Loan, Charles (Cornell University, 198410)The computation of the CS decomposition is the key to the stable computation of the Generalized Singular Value Decomposition, and is also important in other applications. This paper describes our implementation of a ...