Implementation of the singular-value decomposition on the Connection Machine CM-2

Chu, N A

Title: Implementation of the singular-value decomposition on the Connection Machine CM-2

Full Record
Other Related Research

Abstract

In modern digital signal processing, the singular value decomposition is increasingly recognized as an important mathematical tool. The true measure of usefulness of such a tool is very much dependent on the ability to compute it at supercomputer throughput rates. This report describes an implementation of the singular value decomposition (SVD) on the Connection Machine CM-2 using parallel Fortran. The algorithm is based on Hestenes's, which is a Jacobi iteration in which pairs of rows are rotated to become orthogonal. The Fortran implementation of this algorithm on a full CM-2 is comparable in execution speed to the Linpack implementation on a Convex C220 processor.

Authors:: Chu, N A

Publication Date:: Thu Apr 11 00:00:00 EDT 1991

Research Org.:: Naval Research Lab., Washington, DC (United States)

OSTI Identifier:: 5439679

Report Number(s):: AD-A-234124/6/XAB; NRL-9318

Resource Type:: Technical Report

Country of Publication:: United States

Language:: English

Subject:: 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; PARALLEL PROCESSING; SIGNALS; DATA PROCESSING; DIGITAL SYSTEMS; FORTRAN; IMPLEMENTATION; MATHEMATICAL MODELS; SUPERCOMPUTERS; COMPUTERS; DIGITAL COMPUTERS; MATHEMATICAL LOGIC; PROCESSING; PROGRAMMING; PROGRAMMING LANGUAGES; 990200* - Mathematics & Computers

Citation Formats


                    Chu, N A. Implementation of the singular-value decomposition on the Connection Machine CM-2.  United States: N. p., 1991. 
        Web.

Copy to clipboard


                    Chu, N A. Implementation of the singular-value decomposition on the Connection Machine CM-2.  United States.

Copy to clipboard


                    Chu, N A. 1991.  
        "Implementation of the singular-value decomposition on the Connection Machine CM-2".  United States.

Copy to clipboard


                    
@article{osti_5439679,

  title        = {Implementation of the singular-value decomposition on the Connection Machine CM-2},

  author       = {Chu, N A},

  abstractNote = {In modern digital signal processing, the singular value decomposition is increasingly recognized as an important mathematical tool. The true measure of usefulness of such a tool is very much dependent on the ability to compute it at supercomputer throughput rates. This report describes an implementation of the singular value decomposition (SVD) on the Connection Machine CM-2 using parallel Fortran. The algorithm is based on Hestenes's, which is a Jacobi iteration in which pairs of rows are rotated to become orthogonal. The Fortran implementation of this algorithm on a full CM-2 is comparable in execution speed to the Linpack implementation on a Convex C220 processor.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/5439679},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Thu Apr 11 00:00:00 EDT 1991},

  month        = {Thu Apr 11 00:00:00 EDT 1991}

}

Copy to clipboard

Technical Report:

Other availability

Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item. Keep in mind that many technical reports are not cataloged in WorldCat.

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

A multiprocessor scheme for the singular value decomposition

Conference Berry, M; Sameh, A

We present a multiprocessor scheme for determining the singular value decomposition of rectangular matrices in which the number of rows is substantially large (or smaller) than the number of columns. In this scheme, we perform an initial QR factorization on the tall matrix (either A or A/sup T/) using a multiprocessor block Householder algorithm. We then use a parallel one-sided Jacobi scheme to orthogonalize the columns of the upper triangular matrix R to yield the factorization RV = U..sigma.., from which the desired singular value decomposition is obtained. Preliminary experiments on an Alliant FX/8 computer system with 8 processors indicatemore »« less
Singular value decomposition utilizing parallel algorithms on graphical processors

Conference Kotas, Charlotte; Barhen, Jacob

One of the current challenges in underwater acoustic array signal processing is the detection of quiet targets in the presence of noise. In order to enable robust detection, one of the key processing steps requires data and replica whitening. This, in turn, involves the eigen-decomposition of the sample spectral matrix, Cx = 1/K xKX(k)XH(k) where X(k) denotes a single frequency snapshot with an element for each element of the array. By employing the singular value decomposition (SVD) method, the eigenvectors and eigenvalues can be determined directly from the data without computing the sample covariance matrix, reducing the computational requirements formore »« less
Finite-precision arithmetic in singular-value decomposition architectures

Thesis/Dissertation Duryea, R

The singular-value decomposition (SVD) is an important matrix algorithm that has many applications in signal processing. However, its use has been limited due to its computational complexity. Several architecture have been proposed to compute the SVD using arrays of parallel processors. This thesis derives requirements for the precision of arithmetic units (AUs) used in SVD arrays and compares the resource requirements of several architectures. The author's results are based on the assumption that he is operating on matrices of quantized data. Since the matrices have quantization errors, he shows that their singular values will have quantization errors as large asmore »« less
Modifying the singular value decompositions on the connection machine

Conference Yoon, P; Barlow, J

A fully parallel algorithm for updating and downdating the singular value decompositions (SVD) of an m-by-n (m {>=} n) A is described. The algorithm involves similar chasing techniques for modifying the SVDs described in, but fewer plane rotations, and can be implemented almost identically for both updating and downdating. Both cyclic and consecutive storage schemes are considered in parallel implementation. We show that the latter scheme outperforms the former on a coarse-grain distributed-memory MIMD multiprocessor. We present the experimental results on the 32-node Connection Machine (CM-5).
Multiprocessor Jacobi algorithms for dense symmetric eigenvalue and singular value decompositions

Conference Berry, M; Sameh, A

Two parallel algorithms are presented based on Jacobi's method for real symmetric matrices to determine the complete eigensystem of a dense real symmetric matrix and the singular value decomposition of rectangular matrices on a multiprocessor. The intent is to study the advantages of using Jacobi and Jacobi-like schemes over new and existing EISPACK and LINPACK routines on an Alliant FX/8 computer system. For the dense symmetric eigenvalue problem, promising results are shown for small-order matrices. A ''one-sided'' Jacobi-like algorithm which produces the singular value decomposition of a rectangular matrix is shown to provide superior performance for rectangular matrices in whichmore »« less

Similar Records