Results 1  10
of
53,521
Sketching Sparse Matrices
, 2013
"... This paper considers the problem of recovering an unknown sparse p ⇥ p matrix X from an m ⇥ m matrix Y = AXBT,whereAand B are known m ⇥ p matrices with m ⌧ p. The main result shows that there exist constructions of the “sketching ” matrices A and B so that even if X has O(p) nonzeros, it can be rec ..."
Abstract
 Add to MetaCart
This paper considers the problem of recovering an unknown sparse p ⇥ p matrix X from an m ⇥ m matrix Y = AXBT,whereAand B are known m ⇥ p matrices with m ⌧ p. The main result shows that there exist constructions of the “sketching ” matrices A and B so that even if X has O(p) nonzeros, it can
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
Abstract

Cited by 750 (23 self)
 Add to MetaCart
We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
Abstract

Cited by 536 (17 self)
 Add to MetaCart
The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
Abstract

Cited by 773 (23 self)
 Add to MetaCart
, the nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
Abstract

Cited by 555 (22 self)
 Add to MetaCart
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
Abstract

Cited by 676 (18 self)
 Add to MetaCart
, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 568 (10 self)
 Add to MetaCart
. In contrast, heuristic attempts to sparsely solve such systems – greedy algorithms and thresholding – perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almostspherical sections in Banach space theory, and deviation bounds for the eigenvalues
Approximating the permanent
 SIAM J. Computing
, 1989
"... Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the ..."
Abstract

Cited by 345 (26 self)
 Add to MetaCart
in the graph. For a wide class of 01 matrices the approximation scheme is fullypolynomial, i.e., runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output. This class includes all dense matrices (those that contain sufficiently many l’s) and almost all sparse
SPARSKIT: a basic tool kit for sparse matrix computations  Version 2
, 1994
"... . This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boei ..."
Abstract

Cited by 314 (22 self)
 Add to MetaCart
. This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell
A sparse matrix arithmetic based on Hmatrices
 I. Introduction to Hmatrices, Computing
, 1999
"... ..."
Results 1  10
of
53,521