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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  ... 

Accelerated parallel and distributed algorithm using limited internal memory for nonnegative matrix factorization

Duy Khuong Nguyen, Tu Bao Ho
2016 Journal of Global Optimization  
Keywords Non-negative 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  ... 
doi:10.1007/s10898-016-0471-z fatcat:x6nyvaic5fhaxk5r7mf6hxvm6m

Parallel alternating iterative algorithms with and without overlapping on multicore architectures

Héctor Migallón, Violeta Migallón, José Penadés
2016 Advances in Engineering Software  
Convergence properties of these methods are established when the 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.  ... 
doi:10.1016/j.advengsoft.2015.10.012 fatcat:i2x3k74hjzagfctv3tane6acoe

Parallel Nonnegative Matrix Factorization via Newton Iteration

Markus Flatz, Marián Vajteršic
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  ... 
doi:10.1142/s0129626416500146 fatcat:44io4ioehbcnjcoqgziacvouoe

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

Duy-Khuong Nguyen, Tu-Bao Ho
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  ... 
arXiv:1506.08938v1 fatcat:hnetbeqcxjgcrgl732gckhxkci

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

Chao Liu, Hung-chih Yang, Jinliang Fan, Li-Wei He, Yi-Min Wang
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 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).  ... 
doi:10.1145/1772690.1772760 dblp:conf/www/LiuYFHW10 fatcat:l26wwhwhhnhhrf5zna4u3xk72u

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.  ... 

SDPARA: SemiDefinite Programming Algorithm paRAllel version

M. Yamashita, K. Fujisawa, M. Kojima
2003 Parallel Computing  
The SDPARA (SemiDefinite Programming Algorithm 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  ... 
doi:10.1016/s0167-8191(03)00087-5 fatcat:dn7g6k2jbzd2hn3ga4bkrw3mc4

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: 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  ... 
doi:10.1016/0024-3795(86)90286-7 fatcat:3ivgcj4ikve65dlalfohnzkv2m

Inexact Block Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization

Qingjiang Shi, Haoran Sun, Songtao Lu, Mingyi Hong, Meisam Razaviyayn
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.  ... 
doi:10.1109/tsp.2017.2731321 fatcat:bbmx2m2e75h5nealzu2jh7fche

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

Jacek Gondzio, Andreas Grothey
2006 Lecture Notes in Computer Science  
Our implementation outperforms the industry-standard optimizer, shows very good 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.  ... 
doi:10.1007/11752578_62 fatcat:oj4sszgopfdexh3iurlfbvro2y

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization [article]

Ramakrishnan Kannan, Grey Ballard, Haesun Park
2016 arXiv   pre-print
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.  ...  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  ... 
arXiv:1609.09154v1 fatcat:xtcsszubtbeafnffj4ogr7wppq

A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization [article]

Ramakrishnan Kannan and Grey Ballard and Haesun Park
2015 arXiv   pre-print
We propose a 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  ... 
arXiv:1509.09313v1 fatcat:uhxr5bd73berxotxgrhdrdpofm

Parallel algorithms in linear algebra [article]

Richard P. Brent
2010 arXiv   pre-print
This report provides an introduction to algorithms for fundamental linear algebra problems on various 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.  ... 
arXiv:1004.5437v1 fatcat:x4iusllb5bbadpj7hodfzh2ys4

Behavioral clusters in dynamic graphs

James P. Fairbanks, Ramakrishnan Kannan, Haesun Park, David A. Bader
2015 Parallel Computing  
In order to successfully implement this method, we develop a feature based pipeline for dynamic graphs and apply 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.  ... 
doi:10.1016/j.parco.2015.03.002 fatcat:6jh5pyamxjerdnr4dsfkxded4m
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