Results 1 
7 of
7
SVDPACKC (Version 1.0) User's Guide
, 1993
"... SVDPACKC comprises four numerical (iterative) methods for computing the singular value decomposition (SVD) of large sparse matrices using ANSI C. This software package implements Lanczos and subspace iterationbased methods for determining several of the largest singular triplets (singular values an ..."
Abstract

Cited by 63 (4 self)
 Add to MetaCart
SVDPACKC comprises four numerical (iterative) methods for computing the singular value decomposition (SVD) of large sparse matrices using ANSI C. This software package implements Lanczos and subspace iterationbased methods for determining several of the largest singular triplets (singular values and corresponding left and rightsingular vectors) for large sparse matrices. The package has been ported to a variety of machines ranging from supercomputers to workstations: CRAY YMP, IBM RS/6000550, DEC 5000100, HP 9000750, SPARCstation 2, and Macintosh II/fx. This document (i) explains each algorithm in some detail, (ii) explains the input parameters for each program, (iii) explains how to compile/execute each program, and (iv) illustrates the performance of each method when we compute lower rank approximations to sparse termdocument matrices from information retrieval applications. A userfriendly software interface to the package for UNIXbased systems and the Macintosh II/fx is als...
Incomplete Factorization Preconditioning For Linear Least Squares Problems
, 1994
"... this paper is the modified version of GramSchmidt orthogonalization with a rejection test applied right after the formation of the offdiagonal elements of the factor R. For a given rejection parameter 0 / 1, the rejection test is: if r ij ! /= k a ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
this paper is the modified version of GramSchmidt orthogonalization with a rejection test applied right after the formation of the offdiagonal elements of the factor R. For a given rejection parameter 0 / 1, the rejection test is: if r ij ! /= k a
Large Scale Sparse Singular Value Computations
 International Journal of Supercomputer Applications
, 1992
"... . In this paper, we present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We particularly emphasize Lanczos and subspace iterationbased methods for determining several of the largest singular triplets (singular ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
. In this paper, we present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We particularly emphasize Lanczos and subspace iterationbased methods for determining several of the largest singular triplets (singular values and corresponding left and rightsingular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography. The target architectures for our implementations of such methods are the Cray2S/4128 and Alliant FX/80. The sparse SVD problem is well motivated by recent informationretrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse termdocument matrices are desired, and by nonlinear inverse problems from seismic tomography applications in which approximate pseudoinverses of large sparse Jacobian matrices are needed. It is hoped that this research will advance the dev...
Computation of the Singular Subspace Associated With the Smallest Singular Values of Large Matrices
, 1993
"... We compare the blockLanczos and the Davidson methods for computing a basis of a singular subspace associated with the smallest singular values of large matrices. We introduce a simple modification on the preconditioning step of Davidson's method which appears to be efficient on a range of large sp ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We compare the blockLanczos and the Davidson methods for computing a basis of a singular subspace associated with the smallest singular values of large matrices. We introduce a simple modification on the preconditioning step of Davidson's method which appears to be efficient on a range of large sparse matrices.
SVDPACKC (Version 1.0) User's Guide
"... SVDPACKC comprises four numerical (iterative) methods for computing the singular value decomposition (SVD) of large sparse matrices using ANSI C. This software package implements Lanczos and subspace iterationbased methods for determining several of the largest singular triplets (singular values an ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
SVDPACKC comprises four numerical (iterative) methods for computing the singular value decomposition (SVD) of large sparse matrices using ANSI C. This software package implements Lanczos and subspace iterationbased methods for determining several of the largest singular triplets (singular values and corresponding left and rightsingular vectors) for large sparse matrices. The package has been ported to a variety of machines ranging from supercomputers to workstations: CRAY YMP, IBM RS/6000550, DEC 5000100, HP 9000750, SPARCstation 2, and Macintosh II/fx. This document (i) explains each algorithm in some detail, (ii) explains the input parameters for each program, (iii) explains how to compile/execute each program, and (iv) illustrates the performance of each method when we compute lower rank approximations to sparse termdocument matrices from information retrieval applications. A userfriendly software interface to the package for UNIXbased systems and the Macintosh II/fx is als...
Estimating the Largest Singular Values/Vectors of Large Sparse Matrices via Modified Moments
, 1996
"... This dissertation considers algorithms for determining a few of the largest singular values and corresponding vectors of large sparse matrices by solving equivalent eigenvalue problems. The procedure is based on a method by Golub and Kent for estimating eigenvalues of equvalent eigensystems using mo ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This dissertation considers algorithms for determining a few of the largest singular values and corresponding vectors of large sparse matrices by solving equivalent eigenvalue problems. The procedure is based on a method by Golub and Kent for estimating eigenvalues of equvalent eigensystems using modified moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel implementations on a network of workstations. However, one potential drawback to this method is that there is no obvious relationship between the modified moments and the eigenvectors. The lack of eigenvector approximations makes deflation schemes difficult, and no robust implementation of the Golub/Kent scheme are currently used in practical applications. Methods to approximate both eigenvalues and eigenvectors using the theory of modified moments in conjunction with the Chebyshev semiiterative method are described in this disseratation. Deflation issues and implicit ...
HK Polytechnic Univ.
"... This paper proposes an algorithm called Imprecise Spectrum Analysis (ISA) to carry out fast dimension reduction for document classification. ISA is designed based on the onesided Jacobi method for Singular Value Decomposition (SVD). To speedup dimension reduction, it simplifies the orthogonalizatio ..."
Abstract
 Add to MetaCart
This paper proposes an algorithm called Imprecise Spectrum Analysis (ISA) to carry out fast dimension reduction for document classification. ISA is designed based on the onesided Jacobi method for Singular Value Decomposition (SVD). To speedup dimension reduction, it simplifies the orthogonalization process of Jacobi computation and introduces a new mapping formula for transforming original documentterm vectors. To improve classification accuracy using ISA, a feature selection method is further developed to make interclass feature vectors more orthogonal in building the initial weighted termdocument matrix. Our experimental results show that ISA is extremely fast in handling large termdocument matrices and delivers better or competitive classification accuracy compared to SVDbased LSI.