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Page 3347 of Mathematical Reviews Vol. , Issue 92f
[page]

1992
*
Mathematical Reviews
*

); Horton, Graham (D-ERL)

*Parallelization*of robust multigrid methods: [LU*factorization*and frequency decomposition method. ... The multigrid method with ILU smoother, and the frequency decomposition method based on a multiple coarse grid correction, were implemented on an MIMD computer with*distributed*shared*memory*using a ring ...##
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Accelerated parallel and distributed algorithm using limited internal memory for nonnegative matrix factorization

2016
*
Journal of Global Optimization
*

Keywords Non-negative

doi:10.1007/s10898-016-0471-z
fatcat:x6nyvaic5fhaxk5r7mf6hxvm6m
*matrix**factorization*· Accelerated anti-lopsided algorithm · Cooridinate descent algorithm ·*Parallel*and*distributed*algorithm ...*Nonnegative**matrix**factorization*(NMF) is a powerful technique for dimension reduction, extracting latent*factors*and learning part-based representation. ... Therefore, in this chapter, we propose an accelerated*parallel*and*distributed*algorithm to learn NMF models W for large datasets. 2.2 Related work of*nonnegative**matrix**factorization*NMF algorithms can ...##
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Parallel alternating iterative algorithms with and without overlapping on multicore architectures

2016
*
Advances in Engineering Software
*

Convergence properties of these methods are established when the

doi:10.1016/j.advengsoft.2015.10.012
fatcat:i2x3k74hjzagfctv3tane6acoe
*matrix*in question is either M-*matrix*or*symmetric**matrix*. ... The reported experiments show the behavior and effectiveness of the designed*parallel*algorithms by exploiting the benefits of shared*memory*inside the nodes of current SMP supercomputers. ... NCD*matrix*.*Distributed**memory*, 8 (8 × 1) nodes. ...##
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Parallel Nonnegative Matrix Factorization via Newton Iteration

2016
*
Parallel Processing Letters
*

*Nonnegative*

*Matrix*

*Factorization*(NMF) can be used to approximate a large

*nonnegative*

*matrix*as a product of two smaller

*nonnegative*matrices. ... This algorithm is suited for

*parallel*execution on shared-

*memory*systems. It was implemented and tested, delivering satisfactory speedup results. ... The goal of

*Nonnegative*

*Matrix*

*Factorization*(NMF) is to represent a large

*nonnegative*

*matrix*in an approximate way as a product of two significantly smaller

*nonnegative*matrices, which are easier to handle ...

##
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Accelerated Parallel and Distributed Algorithm using Limited Internal Memory for Nonnegative Matrix Factorization
[article]

2015
*
arXiv
*
pre-print

*Nonnegative*

*matrix*

*factorization*(NMF) is a powerful technique for dimension reduction, extracting latent

*factors*and learning part-based representation. ... For large datasets, NMF performance depends on some major issues: fast algorithms, fully

*parallel*

*distributed*feasibility and limited internal

*memory*. ... and

*Distribution*: The proposed algorithms are fully

*parallel*and

*distributed*on limited internal

*memory*systems, which is crucial for big data when computing nodes having limited internal

*memory*that ...

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Distributed nonnegative matrix factorization for web-scale dyadic data analysis on mapreduce

2010
*
Proceedings of the 19th international conference on World wide web - WWW '10
*

We therefore in this paper report our efforts on scaling up the

doi:10.1145/1772690.1772760
dblp:conf/www/LiuYFHW10
fatcat:l26wwhwhhnhhrf5zna4u3xk72u
*nonnegative**matrix**factorization*(NMF) technique. ... We show that by carefully partitioning the data and arranging the computations to maximize data locality and*parallelism*,*factorizing*a tens of millions by hundreds of millions*matrix*with billions of ... Definition 1 (*Nonnegative**Matrix**Factorization*). ...##
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Page 1706 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

First, the

*parallel*shared mem- 65 NUMERICAL ANALYSIS 1706 ory implementation for the Cray X-MP is considered in detail and then some aspects of implementation for*distributed**memory*sys- tems where the ... 95c:65071 a*symmetric*, positive definite*matrix*by reduction of certain posi- tive off-diagonal entries and diagonal compensation of these same entries yield an M-*matrix*. ...##
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SDPARA: SemiDefinite Programming Algorithm paRAllel version

2003
*
Parallel Computing
*

The SDPARA (SemiDefinite Programming Algorithm

doi:10.1016/s0167-8191(03)00087-5
fatcat:dn7g6k2jbzd2hn3ga4bkrw3mc4
*PARAllel*version) is a*parallel*version of the SDPA on multiple processors and*distributed**memory*, which replaces these two parts by their*parallel*implementation ... In execution of the SDPA applied to large scale SDPs, the computation of the so-called Schur complement*matrix*and its Cholesky*factorization*consume most of computational time. ... Since ScaLAPACK assumes the elements of a positive definite*matrix*to be*factorized*are*distributed*according to the two-dimensional block-cyclic*distribution*over*distributed**memory*, what the SDPARA needs ...##
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Author index to volumes 61–80 (1984–1986)

1986
*
Linear Algebra and its Applications
*

GENDREAU, MICHEL: On the Location of Eigen-Values of Off-Diagonal Constant Matrices, 79:99 (1986) GEORGE, ALAN, HEATH, MICHAEL T., AND LIU, JOSEPH:

doi:10.1016/0024-3795(86)90286-7
fatcat:3ivgcj4ikve65dlalfohnzkv2m
*Parallel*Cholesky*Factorization*on a Shared-*Memory*Multiprocessor ... of a*Matrix*on a*Parallel*Computer, 77:341 (1986) Sco-rr, DAVID S.: On the Accuracy of the Gerschgorin Circle Theorem for Bounding the Spread of a Real*Symmetric**Matrix*, 65: 147 (1985 ...##
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Inexact Block Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization

2017
*
IEEE Transactions on Signal Processing
*

*Symmetric*

*nonnegative*

*matrix*

*factorization*(SNMF) is equivalent to computing a

*symmetric*

*nonnegative*low rank approximation of a data similarity

*matrix*. ... It inherits the good data interpretability of the well-known

*nonnegative*

*matrix*

*factorization*technique and have better ability of clustering nonlinearly separable data. ... This motivates the great interests in the application of

*nonnegative*

*matrix*

*factorization*(NMF) to clustering. ...

##
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Direct Solution of Linear Systems of Size 109 Arising in Optimization with Interior Point Methods
[chapter]

2006
*
Lecture Notes in Computer Science
*

Our implementation outperforms the industry-standard optimizer, shows very good

doi:10.1007/11752578_62
fatcat:oj4sszgopfdexh3iurlfbvro2y
*parallel*efficiency on massively*parallel*architecture and solves problems of unprecedented sizes reaching 10 9 variables ... Hence the well-understood*parallel*computing techniques developed for positive definite matrices can be extended to this class of indefinite matrices. ... The corresponding*matrix*H can be reordered leading to structures which can be exploited by a*parallel**factorization*. ...##
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MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization
[article]

2016
*
arXiv
*
pre-print

Non-negative

arXiv:1609.09154v1
fatcat:xtcsszubtbeafnffj4ogr7wppq
*matrix**factorization*(NMF) is the problem of determining two non-negative low rank*factors*W and H, for the given input*matrix*A, such that A ≈ W H. ... It maintains the data and*factor*matrices in*memory*(*distributed*across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild ... One of the popular techniques for collaborative filtering is*matrix**factorization*, often with*nonnegativity*constraints, and its implementation is widely available in many off-the-shelf*distributed*machine ...##
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A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization
[article]

2015
*
arXiv
*
pre-print

We propose a

arXiv:1509.09313v1
fatcat:uhxr5bd73berxotxgrhdrdpofm
*distributed*-*memory**parallel*algorithm that computes the*factorization*by iteratively solving alternating non-negative least squares (NLS) subproblems for W and H. ... Non-negative*matrix**factorization*(NMF) is the problem of determining two non-negative low rank*factors*W and H, for the given input*matrix*A, such that A ≈ W H. ... If k < mn/p, then any*distributed*-*memory**parallel*algorithm on p processors that load balances the*matrix**distributions*and computes W T A and/or AH T must communicate at least Ω(min{ mnk 2 /p, nk}) words ...##
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Parallel algorithms in linear algebra
[article]

2010
*
arXiv
*
pre-print

This report provides an introduction to algorithms for fundamental linear algebra problems on various

arXiv:1004.5437v1
fatcat:x4iusllb5bbadpj7hodfzh2ys4
*parallel*computer architectures, with the emphasis on*distributed*-*memory*MIMD machines. ... In addition, we describe some*parallel*algorithms for orthogonal (QR)*factorization*and the singular value decomposition (SVD). ... On*parallel*machines with*distributed**memory*, questions of data*distribution*and data movement are very important. ...##
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Behavioral clusters in dynamic graphs

2015
*
Parallel Computing
*

In order to successfully implement this method, we develop a feature based pipeline for dynamic graphs and apply

doi:10.1016/j.parco.2015.03.002
fatcat:6jh5pyamxjerdnr4dsfkxded4m
*Nonnegative**Matrix**Factorization*(NMF) to these features. ... This paper contributes a method for combining sparse*parallel*graph algorithms with dense*parallel*linear algebra algorithms in order to understand dynamic graphs including the temporal behavior of vertices ... on*distributed**memory*systems, that are familiar to those working on*parallel*graph algorithms for scale free graphs. ...
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