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 iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular vectors) for large sparse matrices. The package has been ported to a variety of machines ranging from supercomputers to workstations: CRAY Y-MP, IBM RS/6000-550, DEC 5000100, HP 9000-750, 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 term-document matrices from information retrieval applications. A user-friendly software interface to the package for UNIX-based systems and the Macintosh II/fx is als...

this paper is the modified version of Gram-Schmidt orthogonalization with a rejection test applied right after the formation of the off-diagonal elements of the factor R. For a given rejection parameter 0 / 1, the rejection test is: if r ij ! /= k a

. 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 iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular 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 Cray-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications in which approximate pseudo-inverses of large sparse Jacobian matrices are needed. It is hoped that this research will advance the dev...

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 iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular vectors) for large sparse matrices. The package has been ported to a variety of machines ranging from supercomputers to workstations: CRAY Y-MP, IBM RS/6000-550, DEC 5000100, HP 9000-750, 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 term-document matrices from information retrieval applications. A user-friendly software interface to the package for UNIX-based systems and the Macintosh II/fx is als...

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 semi-iterative method are described in this disseratation. Deflation issues and implicit ...

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 one-sided 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 inter-class feature vectors more orthogonal in building the initial weighted term-document matrix. Our experimental results show that ISA is extremely fast in handling large term-document matrices and delivers better or competitive classification accuracy compared to SVD-based LSI.