www.elsevier.com/locate/laa
Least Squares Problems Gauss Quadrature Rules (2009)
Gene Golub, Sungeun Jo, Zheng Su
Ordinary/Data/Total least squares SVD solutions Secular equation approaches “Inverse ” least squares Gauss Quadrature Rules Gauss quadrature theory Tri-diagonalization for orthonormal polynomials...
Geometric Sparsity and Mimetic (2009)
Notion of geometric sparsity — accounting for sparse matrix representation of linear maps using underlying geometry of problem. A geometrically sparse matrix with a scale parameter r0 has the...
Fifty years after the invention of the QR algorithm by John Francis and Vera Kublanovskaya we reconstruct the ideas and the influences that led to its genesis from the originators’ own...
Pierre Comon, Gene Golub, Lek-heng Lim, Bernard Mourrain
Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric...
Twenty-Plus Years of Netlib and NA-Net (2008)
Jack Dongarra, Gene Golub, Eric Grosse, Cleve Moler, Keith Moore
The Netlib software repository was created in 1984 to facilitate quick distribution of public domain software routines for use in scientific computation. The Numerical Analysis Net (or "NA...
On the spectra of the Laplacian matrices of a certain class (2008)
E. E. Tyrtyshnikov, Neurok Techsoft, Gene Golub, Rafig Agaev
A Laplacian matrix L = (ℓij) ∈ R n×n has nonpositive off-diagonal entries and zero row sums. Let Lα = (lij) be a Laplacian matrix defined as
Three results on the PageRank vector: eigenstructure, sensitivity, and the derivative (2008)
David Gleich, Peter Glynn, Gene Golub, Chen Greif
Abstract. The three results on the PageRank vector are preliminary but shed light on the eigenstructure of a PageRank modified Markov chain and what happens when changing the teleportation parameter...
Symmetric tensors and symmetric tensor rank (2008)
Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a sum of symmetric outer...
Ar Kamvar, Taher Haveliwala, Gene Golub
We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while relatively few...
ICNAAM-2004 0 0–4 Inverting a multidimensional shape from moments (2008)
Annie Cuyt, Gene Golub, Peyman Milanfar, Brigitte Verdonk
The problem of reconstructing a function and/or its domain given its moments is encountered in many areas. Several applications from diverse areas such as probability and statistics [4], signal...
MULTIDIMENSIONAL INTEGRAL INVERSION, WITH APPLICATIONS IN SHAPE RECONSTRUCTION ∗ (2008)
Annie Cuyt, Gene Golub, Peyman Milanfar, Brigitte Verdonk
Abstract. In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. It allows one to reconstruct the shape of a quite general object from the knowledge of its Radon...
Symmetric tensors and symmetric tensor rank (2008)
Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer...
Symmetric tensors and symmetric tensor rank (2008)
Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer...
And by contacting: The MIMS Secretary (2008)
Nicholas J. Higham, Mims Eprint, An Interview, Gene Golub, Nicholas J. Higham
On July 3, 2005 I interviewed Gene Golub (1932–2007) during a visit he made to The University of Manchester to attend a workshop. This document provides an edited transcript of the interview. The...
A QR-Like SVD Algorithm for a Product/Quotient of Several Matrices (2007)
Gene Golub, Knut Sølna, Paul Van Dooren
. In this paper we derive a new algorithm for constructing unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left and right...
From Numerical Analysis to Computational Science (2007)
The modern development of numerical computing is driven by the rapid increase in computer performance. The present exponential growth approximately follows Moore’s law, doubling in capacity every...
In many image restoration/superresolution applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or known only to within a set of parameters. We...
Matrix Factorizations in Fixed Point on the C6x VLIW Architecture (2007)
We investigated matrix factorization in three applications: mimimum mean square error decision feedback equalization (which uses a special form of the Cholesky factorization), code division multiple...
Matrix Factorizations in Fixed Point on the C6x VLIW Architecture (2007)
We investigated matrix factorization in three applications: mimimum mean square error decision feedback equalization (which uses a special form of the Cholesky factorization), code division multiple...
Netlib and NA-Net: building a scientific computing community (2007)
Jack Dongarra, G Golub, C Moler, K Moore, Mims Eprint, Jack Dongarra, ...
The Netlib software repository was created in 1984 to facilitate quick distribution of public domain software routines for use in scientific computation. The Numerical Analysis Net (or "NA...
Raf Vandebril, Gene Golub, Marc Van Barel, Raf Vandebril, Gene Golub, Marc Van Barel, ...
On solving the definite tridiagonal
Three results on the PageRank vector: eigenstructure, sensitivity, and the derivative (2007)
Gleich, David, Glynn, Peter, Golub, Gene, Greif, Chen
The three results on the PageRank vector are preliminary but shed light on the eigenstructure of a PageRank modified Markov chain and what happens when changing the teleportation parameter in the...
Genericity and Rank Deficiency of High Order Symmetric Tensors (2006)
Comon, Pierre, Mourrain, Bernard, Lim, Lek-Heng, Golub, Gene
Blind Identification of Under-Determined Mixtures (UDM) is involved in numerous applications, including Multi-Way factor Analysis (MWA) and Signal Processing. In the latter case, the use of...
Symmetric tensors and symmetric tensor rank (2006)
Pierre Comon, Gene Golub, Lek-heng Lim, Bernard Mourrain
Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric...
Multilinear Least Square, Eigenvalue, and Singular Value Problems (2006)
Lek-heng Lim, Vin De Silva, Gene Golub, Liqun Qi, Michael Saunders, ...
aij
A bibliography on semiseparable (2004)
Raf Vandebril, Marc Van Barel, Gene Golub, Nicola Mastronardi, Raf Vandebril, Marc Van Barel, ...
matrices
Adaptive methods for the computation of PageRank (2003)
Ar Kamvar, Taher Haveliwala, Gene Golub
Abstract. We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while...
Adaptive methods for the computation of PageRank (2003)
Ar Kamvar, Taher Haveliwala, Gene Golub
Abstract. We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while...
Computing PageRank using power extrapolation (2003)
Taher Haveliwala, Ar Kamvar, Dan Klein, Chris Manning, Gene Golub
Abstract. We present a novel technique for speeding up the computation of PageRank, a hyperlink-based estimate of the "importance " of Web pages, based on the ideas presented in...
Computing PageRank using power extrapolation (2003)
Taher Haveliwala, Ar Kamvar, Dan Klein, Chris Manning, Gene Golub
Abstract. We present a novel technique for speeding up the computation of PageRank, a hyperlink-based estimate of the “importance ” of Web pages, based on the ideas presented in [7]. The original...
Adaptive methods for the computation of PageRank (2003)
Ar Kamvar, Taher Haveliwala, Gene Golub
Abstract. We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while...
Rank Degeneracy and Least Squares Problems. (2002)
Golub,Gene, Klema,Virginia, Stewart,G. W.
This paper is concerned with least squares problems when the least squares matrix A is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain...
Separable Nonlinear Least Squares: the Variable Projection Method and its Applications (2002)
this paper nonlinear data fitting problems which have as their underlying model a linear combination of nonlinear functions. More generally, one can also consider that there are two sets of unknown...
A computationally efficient superresolution image reconstruction algorithm (2001)
Nhat Nguyen, Peyman Milanfar, Senior Member, Gene Golub
Abstract—Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution [9], [11], [18], [27], [30] had not...
Nhat Nguyen, Peyman Milanfar, Senior Member, Gene Golub
Abstract—In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set...
Nhat Nguyen, Peyman Milanfar, Gene Golub
In many image restoration/superresolution applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or known only to within a set of parameters. We...
A Computationally Efficient Superresolution Image Reconstruction Algorithm (2000)
Nhat Nguyen, Peyman Milanfar, Gene Golub
Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution had not adequately addressed the computational and...
Computer Science, Gene Golub, Paul Van Dooren
. In this paper we derive a new algorithm for constructing a unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left and...
Computing the SVD of a General Matrix Product/Quotient (2000)
Gene Golub, Knut Sølna, Paul Van Dooren
. In this paper we derive a new algorithm for constructing a unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left and...
Dooren, Computing the SVD of a general matrix product/quotient (2000)
Gene Golub, Knut Sølna, Van Dooren
Abstract. In this paper we derive a new algorithm for constructing a unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left...
Dooren, Computing the SVD of a general matrix product/quotient (2000)
Gene Golub, Knut Sølna, Van Dooren
Abstract. In this paper we derive a new algorithm for constructing a unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left...
Blind Superresolution with Generalized Cross-Validation using Gauss-Type Quadrature Rules (1999)
Nhat Nguyen, Peyman Milanfar, Gene Golub
| Superresolution reconstruction produces a high resolution image from a set of aliased low resolution images. We model the low resolution frames as blurred and down-sampled, shifted versions of the...
A Computationally Efficient Superresolution Image Reconstruction Algorithm (1999)
Peyman Milanfar, Nhat Nguyen, Gene Golub, Gene Golub, Scienti Computing, Computational Mathematics
Superresolution reconstruction produces a high resolution image from a set of low resolution images. Previous work on superresolution [6, 10, 17, 23, 27] had not adequately addressed the...
A Parallel Balanced Method for Sparse Linear Systems (1997)
Vivek Sarin, Ahmed Sameh, Gene Golub
A scalable parallel algorithm is proposed for the solution of general, nonsingular sparse linear systems. The linear system is partitioned into blocks of rows with a small number of unknowns common...
Inner and outer iterations for the Chebyshev algorithm (1995)
Gene Golub, Joseph Keller, Eldar Giladi, Eldar Giladi, Gene H. Golub, Joseph B. Keller
We analyze the Chebyshev iteration in which the linear system involving the splitting matrix is solved inexactly by an inner iteration. We assume that the tolerance for the inner iteration may change...
The periodic Schur decomposition. Algorithms and applications (1992)
Adam Bojanczyk, Gene Golub, Paul Van Dooren
. In this paper we derive a unitary eigendecomposition for a sequence of matrices which we call the periodic Schur decomposition. We prove its existence and discuss its application to the solution of...
Direct Block Tridiagonalization of Single-Input Single-Output Systems (1992)
Gene Golub, Bo Kågström, Paul Van Dooren
: In this paper we derive a direct method for block tridiagonalizing a single-input single-output system triple fA; b; cg. The method is connected to the nonsymmetric Lanczos procedure developed in...
Rank Degeneracy and Least Squares Problems (1976)
Gene Golub, Virginia Klema, G. W. Stewart
This paper is concerned with least squares problems when the least squares matrix A is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain...
Rosetak Document 4: Rank Degeneracies and Least Square Problems
Gene Golub, Virginia Klema, G. W. Stewart
In this paper we shall be concerned with the following problem. Let A be an m x n matrix with m being greater than or equal to n, and suppose that A is near (in a sense to be made precise later) a...
Some Large Scale Matrix Computation Problems
Zhaojun Bai, Mark Fahey, Gene Golub
The central mathematical problem of this report is to bound the quantity u T f(A)v, where A is a given n \Theta n real matrix, u and v are given n-vectors, and f is a given smooth function....
Tikhonov Regularization And Total Least Squares
Gene Golub, Per Christian Hansen
. Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary...
Some Large Scale Matrix Computation Problems
Zhaojun Bai, Mark Fahey, Gene Golub
There are numerous applications in physics, statistics and electrical circuit simulation where it is required to bound entries and the trace of the inverse and the determinant of a large sparse...
Tikhonov Regularization And Total Least Squares
Gene Golub, Per Christian Hansen
. Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary...
Some Large Scale Matrix Computation Problems
Zhaojun Bai, Mark Fahey, Gene Golub
Introduction The central problem studied in this chapter is to estimate a lower bound L and/or an upper bound U , such that L u T f(A)v U; (1) where A is an n \Theta n given real matrix, u and v are...