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DECOMP: an implementation of Dantzig-Wolfe decomposition for linear programming

<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2fqqu5s6wbgk5gcucpt3wqm3gy" style="color: black;">European Journal of Operational Research</a> </i> &nbsp;
Stochastic linear programming using importance sampling and parallel computation.  ...  Implementation of DECUBE, a linear programming decomposition code in Fortran on an Intel iPSC/2 Hypercube computer with 64 processors.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-2217(90)90023-5">doi:10.1016/0377-2217(90)90023-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hxmb53j7mbehbctacknhc27evq">fatcat:hxmb53j7mbehbctacknhc27evq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170924124230/http://www.dtic.mil/get-tr-doc/pdf?AD=ADA225675" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c0/60/c06048a4e1f653deef52b281362b6df7e723bc2e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-2217(90)90023-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Investigation of the performance of LU decomposition method using CUDA

Caner Ozcan, Baha Sen
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kcayf4mk7zbrbhvdwizgrxaruu" style="color: black;">Procedia Technology - Elsevier</a> </i> &nbsp;
In recent years, parallel processing has been widely used in the computer industry.  ...  In this study Graphics Processing Units (GPU) accelerated implementation of LU linear algebra routine is implemented. LU decomposition is a decomposition of the form A=LU where A is a square matrix.  ...  CUDA programming model allows us to execute thousands of threads simultaneously on the GPU. CUDA organizes a parallel computation using the abstractions of threads, blocks and grids.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.protcy.2012.02.011">doi:10.1016/j.protcy.2012.02.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jaokyfnzlnbrngpgronwgie7zm">fatcat:jaokyfnzlnbrngpgronwgie7zm</a> </span>
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Research on Parallel LU Decomposition Method and It's Application in Circle Transportation

Aimin Yang, Chunfeng Liu, Jincai Chang, Xiaoqiang Guo
<span title="2010-11-01">2010</span> <i title="International Academy Publishing (IAP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jr7366lnajgfrhmmgwgrpt3o7u" style="color: black;">Journal of Software</a> </i> &nbsp;
This paper mainly designed a new method of using the Parallel LU Decomposition Algorithm for solving large-scale dense linear equations on the basis of the strategy of divide and rule,and analyzed the  ...  In addition, the extension of Parallel LU Decomposition Algorithm, opened up a new idea of solving large-scale dense linear equations .This paper firstly introduced a solving method-LU decomposition algorithm  ...  This chapter presents the transportation in linear programming, the transportation problem of circular solving linear equations using parallel LU decomposition algorithm for solving the solution, improve  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4304/jsw.5.11.1250-1255">doi:10.4304/jsw.5.11.1250-1255</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cxx4rwqxsvdbdgtsxez2okrwxi">fatcat:cxx4rwqxsvdbdgtsxez2okrwxi</a> </span>
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Data and computation transformations for multiprocessors

Jennifer M. Anderson, Saman P. Amarasinghe, Monica S. Lam
<span title="">1995</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a3hx753rrfdorizx3a3ovuee4y" style="color: black;">Proceedings of the fifth ACM SIGPLAN symposium on Principles and practice of parallel programming - PPOPP &#39;95</a> </i> &nbsp;
Using the linear algebra model, the algorithm generates a system of equations that specifies the conditions the desired decompositions must satisfy.  ...  A key issue in programming these machines is selecting the computation decomposition and data decomposition, the mapping of the computation and data, respectively, across the processors of the machine.  ...  Statement To achieve good performance on parallel systems, programs must make effective use of the computer's memory hierarchy as well as its ability to perform computation in parallel.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/209936.209954">doi:10.1145/209936.209954</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ppopp/AndersonAL95.html">dblp:conf/ppopp/AndersonAL95</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cago5ajcrzcfvkfx3d3drqpp24">fatcat:cago5ajcrzcfvkfx3d3drqpp24</a> </span>
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numpywren: serverless linear algebra [article]

Vaishaal Shankar, Karl Krauth, Qifan Pu, Eric Jonas, Shivaram Venkataraman, Ion Stoica, Benjamin Recht, Jonathan Ragan-Kelley
<span title="2018-10-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Linear algebra operations are widely used in scientific computing and machine learning applications.  ...  We show that, for certain linear algebra algorithms such as matrix multiply, singular value decomposition, and Cholesky decomposition, numpywren's performance (completion time) is within 33% of ScaLAPACK  ...  Acknowledgements This research is supported in part by ONR awards N00014-17-1-2191, N00014-17-1-2401, and N00014-18-1-2833, the DARPA Assured Autonomy (FA8750-18-C-0101) and Lagrange (W911NF-16-1-0552) programs  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1810.09679v1">arXiv:1810.09679v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lxv65s42rzd6vomkg2pff2akhm">fatcat:lxv65s42rzd6vomkg2pff2akhm</a> </span>
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Performance analysis of a parallel Dantzig-Wolfe decomposition algorithm for linear programming

Jung Lyu, Hsing Luh, Ming-Chang Lee
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nkrwe4pmozafvnd72yxufztpku" style="color: black;">Computers and Mathematics with Applications</a> </i> &nbsp;
This paper employs the Dantzig-Wolfe decomposition principle to solve linear programming models in a parallel-computing environment.  ...  Adopting the queuing discipline, we showed that under very general conditions, the proposed algorithm speedup trends toward a limiting value as the number of processors increases. (~)  ...  This research, therefore, provides an upper bound for algorithm speedup using parallel processing for linear programs• A PARALLEL LP ALGORITHM In problem (1), let each Ai have mi rows and pi columns  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0898-1221(02)00267-5">doi:10.1016/s0898-1221(02)00267-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s57ne5lpsbhyve3bkzzkx5tuza">fatcat:s57ne5lpsbhyve3bkzzkx5tuza</a> </span>
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AUTOMATIC DATA AND COMPUTATION DECOMPOSITION FOR DISTRIBUTED-MEMORY MACHINES

QI NING, VINCENT VAN DONGEN, GUANG R. GAO
<span title="">1995</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x6p3xmf7graczk5begbrisonce" style="color: black;">Parallel Processing Letters</a> </i> &nbsp;
Within each cluster of loop nests, decomposition and data locality constraints are formulated as a system of homogeneous linear equations which is solved by polynomial time algorithms.  ...  This work is central to the on-going compiler development effort under the EPPP (Environment for Portable Parallel Programming) Project'. A brief discussion of the current implementation is included.  ...  Acknowledgment We would like to thank Chris Freehill for providing us his benchmark testing results and for proofreading.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0129626495000485">doi:10.1142/s0129626495000485</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/za7xw7zpwnf7jemhjzhdtrgz6u">fatcat:za7xw7zpwnf7jemhjzhdtrgz6u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170817063904/https://www.computer.org/csdl/proceedings/hicss/1995/6935/00/69350103.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2a/00/2a00623aff8c1eccaccbe84f85cc8029cb60f6a4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0129626495000485"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

On Speed versus Accuracy: Some Case Studies

Mauro Leoncini
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hhnp3o4qcjfyfd4gpifcdou6ui" style="color: black;">Journal of Complexity</a> </i> &nbsp;
More precisely, we focus on a set of significant examples and prove that: (1) the fastest known polynomial evaluation algorithms are not stable, (2) LUP decomposition cannot be computed stably in polylogarithmic  ...  parallel time, and (3) reductions among computational problems do not in general constitute a practical tool for solving numerical problems.  ...  In Section 3 we deal with parallel algorithms for computing the PLU decomposition of a real matrix.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jcom.1996.0016">doi:10.1006/jcom.1996.0016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mss7vwdmivdlph7dcpphmfcegm">fatcat:mss7vwdmivdlph7dcpphmfcegm</a> </span>
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Object-Oriented parallel CFD with JAVA [chapter]

D. Eyheramendy
<span title="">2004</span> <i title="Elsevier"> Parallel Computational Fluid Dynamics 2003 </i> &nbsp;
In this paper, we would like to address the problem of the use of modern software environments in engineering sciences, and more precisely in computational fluid dynamics.  ...  The use of multi-threading in JAVA is illustrated on a Schwartz overlapping domain decomposition method for a stabilized finite elements formulation for the Navier-Stokes equations.  ...  A direct linear system solver based on a Crout decomposition is used to solve the linear system at each iteration. Results are obtained using a ramping technique to achieve Re 10000.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/b978-044451612-1/50052-4">doi:10.1016/b978-044451612-1/50052-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lvlvhekopbf6ddhsjknapctjzq">fatcat:lvlvhekopbf6ddhsjknapctjzq</a> </span>
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Parallel Multistage Preconditioners Based on a Hierarchical Graph Decomposition for SMP Cluster Architectures with a Hybrid Parallel Programming Model [chapter]

Kengo Nakajima
<span title="">2007</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this work, the Parallel Hierarchical Interface Decomposition Algorithm (PHIDAL) and a hybrid parallel programming model were applied to finite-element based simulations of linear elasticity problems  ...  in media with heterogeneous material properties using parallel preconditioned iterative solvers.  ...  National Laboratory, for use of their computer resources.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-75444-2_39">doi:10.1007/978-3-540-75444-2_39</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oq3qgaoz7ngadevvqiiuxzljpu">fatcat:oq3qgaoz7ngadevvqiiuxzljpu</a> </span>
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Solving Linear Programming Problems on the Parallel Virtual Machine Environment

JrJung Lyu, Hsing Luh, Ming-Chang Lee
<span title="2004-02-01">2004</span> <i title="Science Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/myyqjkgwizb57p75zpb2nhqvpe" style="color: black;">American Journal of Applied Sciences</a> </i> &nbsp;
This study developed a parallel algorithm to efficiently solve linear programming models.  ...  The empirical results demonstrate that the speedup of this parallel algorithm approaches linearity, which means that it can take full advantage of the distributed computing power as the size of the problem  ...  In this study, we developed a parallel algorithm, based on the Dantzig-Wolfe Decomposition Principle (DWDP), to solve linear programming and other blocktype optimization problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3844/ajassp.2004.90.94">doi:10.3844/ajassp.2004.90.94</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tq4xtfgdqjgh3ohwl5qlpdj64m">fatcat:tq4xtfgdqjgh3ohwl5qlpdj64m</a> </span>
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Two-Stage Least Squares Algorithms with QR Decomposition for Simultaneous Equations Models on Heterogeneous Multicore and Multi-GPU Systems

Carla Ramiro, Jose J. López-Espín, Domingo Giménez, Antonio M. Vidal
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cx3f4s3qmfe6bg4qvuy2cxezyu" style="color: black;">Procedia Computer Science</a> </i> &nbsp;
This paper analyzes the use of a multicore+multiGPU system for solving Simultaneous Equations Models by the Two-Stage Least Squares method with QR decomposition.  ...  The combination of CPU and GPU allows us to reduce the execution time in the solution of large SEM.  ...  models One of the most decisive concepts for successfully programming a computer that uses GPU and multicore processors is the underlying model of the parallel computer.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procs.2012.04.223">doi:10.1016/j.procs.2012.04.223</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eujlbepmfrgr7kq3b3b7vbjhmq">fatcat:eujlbepmfrgr7kq3b3b7vbjhmq</a> </span>
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Parallel Algorithms for Graph Optimization Using Tree Decompositions

Blair D. Sullivan, Dinesh Weerapurage, Chris Groer
<span title="">2013</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t3x4vqewrncrfgn2wu7cafsbsq" style="color: black;">2013 IEEE International Symposium on Parallel &amp; Distributed Processing, Workshops and Phd Forum</a> </i> &nbsp;
This work was performed while all three authors were at Oak Ridge National Laboratory, and was funded by the Department of Energy Office of Science, Office of Advanced Scientific Computing Research under  ...  a grant through the Applied Mathematics Program.  ...  Task-oriented parallel dynamic programming Having described our novel ideas for parallelizing the construction of tree decompositions, we now move on to our approach for applying distributed computing  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdpsw.2013.242">doi:10.1109/ipdpsw.2013.242</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ipps/SullivanWG13.html">dblp:conf/ipps/SullivanWG13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vvu3wqxhfnhn3awwxsllsrddna">fatcat:vvu3wqxhfnhn3awwxsllsrddna</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180729032809/https://digital.library.unt.edu/ark:/67531/metadc830645/m2/1/high_res_d/1042920.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9e/ed/9eed2df8253476110bc3164ff12701ec7f963217.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdpsw.2013.242"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Parallel Processing Model for Cholesky Decomposition Algorithm in AlgoWiki Project

<span title="">2016</span> <i title="FSAEIHE South Ural State University (National Research University)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ut52ymkqynfbhjyzwhwl44xhvq" style="color: black;">Supercomputing Frontiers and Innovations</a> </i> &nbsp;
The comprehension of the parallel algorithm structure enable us to implement efficiently the algorithm at hardware platform specified.  ...  A detailed analysis of information graph, data structure, memory access profile, computation locality, scalability and other algorithm properties is conducted, which allows us to demonstrate a lot of unevident  ...  This paper is distributed under the terms of the Creative Commons Attribution-Non Commercial 3.0 License which permits non-commercial use, reproduction and distribution of the work without further permission  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14529/jsfi160307">doi:10.14529/jsfi160307</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yvjcte3ywnchpai5gvz7f5dypa">fatcat:yvjcte3ywnchpai5gvz7f5dypa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721205522/http://superfri.org/superfri/article/download/110/212" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5c/01/5c011a05a2a20ed39b2b214dddfc5c79bb3ac1f3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14529/jsfi160307"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

A Multi Core Hyper-Threaded Solution of a System of Linear Equations for Intelx64 Architecture

Richa Singhal, Dr. Sanjeev Bansal
<span title="">2014</span> <i title="IOSR Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vabuspdninc75epczdurccts4u" style="color: black;">IOSR Journal of Computer Engineering</a> </i> &nbsp;
The paper targets solving a system of linear equations for a multi core INTELx64 architecture with hyper threading using standard LU decomposition methodology.  ...  The sample uses as input a matrix of 4000x4000 double precision floating point representation of the system.  ...  LU Decomposition To solve the basic model of parallel LU decomposition as suggested above was adopted.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9790/0661-16422126">doi:10.9790/0661-16422126</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/45xwx56zzfctjomond6zszyi2u">fatcat:45xwx56zzfctjomond6zszyi2u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180602095639/http://www.iosrjournals.org/iosr-jce/papers/Vol16-issue4/Version-2/E016422126.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/4f/e54f93bb2d35861dca8f873c81f5c131458997aa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9790/0661-16422126"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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