Results 1  10
of
87
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 me ..."
Abstract

Cited by 534 (14 self)
 Add to MetaCart
. 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 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 by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
Applied Numerical Linear Algebra
 Society for Industrial and Applied Mathematics
, 1997
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We rst discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing e cient algorithms. We illustrate ..."
Abstract

Cited by 531 (26 self)
 Add to MetaCart
We survey general techniques and open problems in numerical linear algebra on parallel architectures. We rst discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing e cient algorithms. We illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem, the nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.
A column approximate minimum degree ordering algorithm
, 2000
"... Sparse Gaussian elimination with partial pivoting computes the factorization PAQ = LU of a sparse matrix A, where the row ordering P is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering, Q, based solely on the nonzero patt ..."
Abstract

Cited by 253 (50 self)
 Add to MetaCart
Sparse Gaussian elimination with partial pivoting computes the factorization PAQ = LU of a sparse matrix A, where the row ordering P is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering, Q, based solely on the nonzero pattern of A such that the factorization remains as sparse as possible, regardless of the subsequent choice of P. The choice of Q can have a dramatic impact on the number of nonzeros in L and U. One scheme for determining a good column ordering for A is to compute a symmetric ordering that reduces fillin in the Cholesky factorization of ATA. This approach, which requires the sparsity structure of ATA to be computed, can be expensive both in
Software Reuse
 ACM Computing Surveys
, 1992
"... Software reuse is the process ofcreating software systems from existing software rather than building software systems from scratch. ‘l’his simple yet powerful vision was introduced in 1968. Software reuse has, however, failed to become a standard software engineering practice. In an attempt to unde ..."
Abstract

Cited by 237 (2 self)
 Add to MetaCart
Software reuse is the process ofcreating software systems from existing software rather than building software systems from scratch. ‘l’his simple yet powerful vision was introduced in 1968. Software reuse has, however, failed to become a standard software engineering practice. In an attempt to understand why, researchers have renewed their interest in software reuse and in the obstacles to implementing it. This paper surveys the different approaches to software reuse found in the research literature. It uses a taxonomy to describe and compare the different approaches and make generalizations about the field of software reuse. The taxonomy characterizes each reuse approach interms of its reusable artifacts and the way these artifacts are abstracted, selected, speciahzed, and integrated. Abstraction plays a central role in software reuse. Concise and expressive abstractions are essential if software artifacts are to be effectively reused. The effectiveness of a reuse technique can be evaluatedin terms of cognztzue dwtancean intuitive gauge of the intellectual effort required to use the technique. Cognitive distance isreduced in two ways: (l) Higher level abstractions ina reuse technique
An UnsymmetricPattern Multifrontal Method for Sparse LU Factorization
 SIAM J. MATRIX ANAL. APPL
, 1994
"... Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops ..."
Abstract

Cited by 117 (27 self)
 Add to MetaCart
Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily on dense matrix kernels exists for matrices whose pattern is very unsymmetric. We address this deficiency and present a new unsymmetricpattern multifrontal method based on dense matrix kernels. As in the classical multifrontal method, advantage is taken of repetitive structure in the matrix by factorizing more than one pivot in each frontal matrix thus enabling the use of Level 2 and Level 3 BLAS. The performance is compared with the classical multifrontal method and other unsymmetric solvers on a CRAY YMP.
Accurate Singular Values of Bidiagonal Matrices
 SIAM J. SCI. STAT. COMPUT
, 1990
"... Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magni ..."
Abstract

Cited by 100 (17 self)
 Add to MetaCart
Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magnitudes. In contrast, the standard algorithm for bidiagonal matrices may compute small singular values with no relative accuracy at all. Numerical experiments show that the new algorithm is comparable in speed to the standard algorithm , and frequently faster.
Self adapting linear algebra algorithms and software
, 2004
"... One of the main obstacles to the efficient solution of scientific problems is the problem of tuning software, both to the available architecture and to the user problem at hand. We describe approaches for obtaining tuned highperformance kernels, and for automatically choosing suitable algorithms. S ..."
Abstract

Cited by 81 (22 self)
 Add to MetaCart
One of the main obstacles to the efficient solution of scientific problems is the problem of tuning software, both to the available architecture and to the user problem at hand. We describe approaches for obtaining tuned highperformance kernels, and for automatically choosing suitable algorithms. Specifically, we describe the generation of dense and sparse blas kernels, and the selection of linear solver algorithms. However, the ideas presented here extend beyond these areas, which can be considered proof of concept.
Fortran codes for estimating the onenorm of a real or complex matrix, with applications to condition estimation
 ACM Trans. Math. Software
, 1988
"... FORTRAN 77 codes SONEST and CONEST are presented for estimating the lnorm (or the mnorm) of a real or complex matrix, respectively. The codes are of wide applicability in condition estimation since explicit access to the matrix, A, is not required; instead, matrixvector products Ax and A “‘n are ..."
Abstract

Cited by 74 (18 self)
 Add to MetaCart
FORTRAN 77 codes SONEST and CONEST are presented for estimating the lnorm (or the mnorm) of a real or complex matrix, respectively. The codes are of wide applicability in condition estimation since explicit access to the matrix, A, is not required; instead, matrixvector products Ax and A “‘n are computed by the calling program via a reverse communication interface. The algorithms are based on a convex optimization method for estimating the lnorm of a real matrix devised by Hager [Condition estimates. SIAM J. Sci. Stat. Comput. 5 (1984), 3113161. We derive new results concerning the behavior of Hager’s method, extend it to complex matrices, and make several algorithmic modifications in order to improve the reliability and efficiency.
ON PROJECTED NEWTON BARRIER METHODS FOR LINEAR PROGRAMMING AND AN EQUIVALENCE TO KARMARKAR'S PROJECTIVE METHOD
, 1986
"... Interest in linear programming has been intensified recently by Karmarkar's publication in 1984 of an algorithm that is claimed to be much faster than the simplex method for practical problems. We review classical barrierfunction methods for nonlinear programming based on applying a logarithmic tra ..."
Abstract

Cited by 67 (8 self)
 Add to MetaCart
Interest in linear programming has been intensified recently by Karmarkar's publication in 1984 of an algorithm that is claimed to be much faster than the simplex method for practical problems. We review classical barrierfunction methods for nonlinear programming based on applying a logarithmic transformation to inequality constraints. For the special case of linear programming, the transformed problem can be solved by a "projected Newton barrier" method. This method is shown to be equivalent to Karmarkar's projective method for a particular choice of the barrier parameter. We then present details of a specific barrier algorithm and its practical implementation. Numerical results are given for several nontrivial test problems, and the implications for future developments in linear programming are discussed.
Software libraries for linear algebra computations on high performance computers
 SIAM REVIEW
, 1995
"... This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed b ..."
Abstract

Cited by 67 (16 self)
 Add to MetaCart
This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed by an outline of ScaLAPACK, which is a distributed memory version of LAPACK currently under development. The importance of blockpartitioned algorithms in reducing the frequency of data movement between different levels of hierarchical memory is stressed. The use of such algorithms helps reduce the message startup costs on distributed memory concurrent computers. Other key ideas in our approach are the use of distributed versions of the Level 3 Basic Linear Algebra Subprograms (BLAS) as computational building blocks, and the use of Basic Linear Algebra Communication Subprograms (BLACS) as communication building blocks. Together the distributed BLAS and the BLACS can be used to construct highe...