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PMIRKDC: a parallel mono-implicit Runge–Kutta code with defect control for boundary value ODEs

P.H. Muir, R.N. Pancer, K.R. Jackson
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sv4mpg7lmfaqdp24ohp5qqiobm" style="color: black;">Parallel Computing</a> </i> &nbsp;
The primary computational costs involve the treatment of large, almost block diagonal (ABD) linear systems.  ...  Other modifications involve parallelization of the setup of the ABD systems and solution interpolants, and defect estimation. Numerical results show almost linear speedups.  ...  Acknowledgements This work is supported by the Natural Sciences and Engineering Research Council of Canada, the Information Technology Research Center of Ontario, and Communications and Information Technology  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8191(03)00038-3">doi:10.1016/s0167-8191(03)00038-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sopcbexl7zc2bhhxzwdyeeeabq">fatcat:sopcbexl7zc2bhhxzwdyeeeabq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070418111810/http://cs.stmarys.ca/~muir/MuirPancerJackson2003.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/92/40/92406c6a950df0cf3efcb9ab145fc0a5db8295ec.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8191(03)00038-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Maintaining LU factors of a general sparse matrix

Philip E. Gill, Walter Murray, Michael A. Saunders, Matgaret H. Wright
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
The updates provided are addition, deletion or replacement of a row or column of A, and rank-one modification. (Previously, column replacement has been the only update available.)  ...  Various design features of the implementation (LUSOL) are described, and computational comparisons are made with the LAOS and MAZB packages of Reid (1976) and Duff (1977) . ing by unit triangular matrices  ...  We are grateful to Robert Burchett, Floyd Chadee, Robert Entriken, Patrick McAllister, Thomas Rutherford, and John Stone for their helpful comments on various procedures j?om LUSOL.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0024-3795(87)90112-1">doi:10.1016/0024-3795(87)90112-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ybaxphcxbbbjpifrac5tyqsjme">fatcat:ybaxphcxbbbjpifrac5tyqsjme</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170930013155/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/851/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDI0Mzc5NTg3OTAxMTIx.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/62/3c/623cfe0b52852f08744d574a61b84c059438ae2c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0024-3795(87)90112-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

PCA for large data sets with parallel data summarization

Carlos Ordonez, Naveen Mohanam, Carlos Garcia-Alvarado
<span title="2013-09-10">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/of3bmcozzfddjojxsoxwzys55y" style="color: black;">Distributed and parallel databases</a> </i> &nbsp;
Benchmarking on multicore CPUs and a parallel DBMS running on multiple nodes confirms linear speedup and linear scalability.  ...  Experiments with large data sets on multicore CPUs show that our solution is much faster than the R statistical package as well as solving PCA with SQL queries.  ...  Acknowledgments This work was supported by NSF grant IIS 0914861.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10619-013-7134-6">doi:10.1007/s10619-013-7134-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aleeiv7g65brpnffeiuezpziv4">fatcat:aleeiv7g65brpnffeiuezpziv4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140312083321/http://www2.cs.uh.edu:80/~ordonez/w-2014-DAPD-udfsvd.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/b4/00/b400927e751ac31cab79691a928d89a34dea8bd1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10619-013-7134-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Combinatorial Problems in Solving Linear Systems [chapter]

Iain Duff, Bora Uçar
<span title="2012-01-25">2012</span> <i title="Chapman and Hall/CRC"> Combinatorial Scientific Computing </i> &nbsp;
As the core of many of today's numerical linear algebra computations consists of the solution of sparse linear system by direct or iterative methods, we survey some combinatorial problems, ideas, and algorithms  ...  Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise.  ...  Amestoy and Jean-Yves L'Excellent for their contribution to the presented material. We also thankÜmit V. Ç atalyürek for his comments on an earlier version of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1201/b11644-3">doi:10.1201/b11644-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wdq7hb343jawxjaqsxz5nihtfq">fatcat:wdq7hb343jawxjaqsxz5nihtfq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170517014930/http://graal.ens-lyon.fr:80/~bucar/papers/duuc-survey.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/fe/b8/feb8c45a6fd1cc8dfa420ba162b0f0fa6027ce6e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1201/b11644-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Multilevel ILU With Reorderings for Diagonal Dominance

Yousef Saad
<span title="">2005</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wbdvoluxebgjhn3wq3qsnldey4" style="color: black;">SIAM Journal on Scientific Computing</a> </i> &nbsp;
This leads to an effective incomplete factorization preconditioner for general nonsymmetric, irregularly structured, sparse linear systems.  ...  The nonsymmetric permutation exploits a greedy strategy to put large entries of the matrix in the diagonal of the upper leading submatrix.  ...  Special thanks to Tim Davis for making these and other linear systems available in his excellent repository of test matrices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/030602733">doi:10.1137/030602733</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3dv2j457offfjjmgzooefoesge">fatcat:3dv2j457offfjjmgzooefoesge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120704043709/http://www-users.cs.umn.edu:80/~saad/PDF/umsi-2003-191-REVIS.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/44/21/44215cbb7d4f0194b804470bf2d2aeea2be2257d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/030602733"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices

Jun Zhang
<span title="">2001</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jkb4mlvirjanvdf6ozhoncfkyq" style="color: black;">SIAM Journal on Matrix Analysis and Applications</a> </i> &nbsp;
The first part with large diagonal dominance is reordered using a graph-based strategy, followed by an ILU factorization.  ...  The whole process is repeated on the Schur complement matrix and continues for a few times to yield a multilevel ILU factorization.  ...  However, the elimination process is only performed with respect to the columns in E, and linear combinations for columns in C are performed accordingly.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0895479899354251">doi:10.1137/s0895479899354251</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sracqx24nzgfxnouqgwptadp5m">fatcat:sracqx24nzgfxnouqgwptadp5m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190308040848/http://pdfs.semanticscholar.org/ec4e/afba64260c958d8748effc909cfe526eff2f.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/ec/4e/ec4eafba64260c958d8748effc909cfe526eff2f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0895479899354251"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Developments and trends in the parallel solution of linear systems

Iain S. Duff, Henk A. van der Vorst
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sv4mpg7lmfaqdp24ohp5qqiobm" style="color: black;">Parallel Computing</a> </i> &nbsp;
We brie y discuss the solution of dense linear systems, before studying the solution of sparse equations by direct and iterative methods.  ...  In this review paper, we consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism.  ...  Acknowledgments We are grateful to Rob Bisseling, Wim Bomhof, Val erie Frayss e, Luc Giraud, Karl Meerbergen, and Denis Trystram for comments on an earlier version of the text.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8191(99)00077-0">doi:10.1016/s0167-8191(99)00077-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3erwohv7r5agthberjgq7v63n4">fatcat:3erwohv7r5agthberjgq7v63n4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170821191951/https://dspace.library.uu.nl/bitstream/handle/1874/2641/parco.pdf?sequence=1" 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/36/7a/367a53111c8e4b94d74d65520962d4464d4f0652.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8191(99)00077-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

ABS methods and ABSPACK for linear systems and optimization: A review

Emilio Spedicato, Elena Bodon, AntoninoDel Popolo, Nezam Mahdavi-Amiri
<span title="">2003</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a7azxtgamnavvcktn5y7xrjas4" style="color: black;">4OR</a> </i> &nbsp;
ABS methods are a large class of methods, based upon the Egervary rank reducing algebraic process, first introduced in 1984 by Abaffy, Broyden and Spedicato for solving linear algebraic systems, and later  ...  In this paper we review ABS methods for linear systems and optimization, from both the point of view of theory and the numerical performance of ABSPACK.  ...  Acknowledgements Work partially supported by ex MURST 60% 2001 funds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10288-002-0004-0">doi:10.1007/s10288-002-0004-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y5flxwfbvndqzna4ouqoscamni">fatcat:y5flxwfbvndqzna4ouqoscamni</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20181030054307/http://cds.cern.ch/record/580769/files/0209241.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/66/81/6681d413df3bdd8d654a64b8d7a588dc307cc514.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10288-002-0004-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

ABS Methods and ABSPACK for Linear Systems and Optimization, a Review [article]

Emilio Spedicato, Nezam Mahdavi-Amiri Department of Mathematics, University of Bergamo, Bergamo;
<span title="2002-09-12">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
ABS methods are a large class of methods, based upon the Egervary rank reducing algebraic process, first introduced in 1984 by Abaffy, Broyden and Spedicato for solving linear algebraic systems, and later  ...  In this paper we review ABS methods for linear systems and optimization, from both the point of view of theory and the numerical performance of ABSPACK.  ...  a mathematical package for solving linear and nonlinear systems and optimization problems using the ABS algorithms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/astro-ph/0209241v1">arXiv:astro-ph/0209241v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6g47taspvjcgtntulzimvr7ige">fatcat:6g47taspvjcgtntulzimvr7ige</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-astro-ph0209241/astro-ph0209241.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> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/astro-ph/0209241v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Pieter Ghysels, Xiaoye S. Li, François-Henry Rouet, Samuel Williams, Artem Napov
<span title="">2016</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wbdvoluxebgjhn3wq3qsnldey4" style="color: black;">SIAM Journal on Scientific Computing</a> </i> &nbsp;
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices.  ...  We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices.  ...  Yvan Notay provided the code to generate the convection diffusion matrices and the code for the Helmholtz problems was provided by Shen Wang.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/15m1010117">doi:10.1137/15m1010117</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wqgn7munmfb7josi3e2ohqg5pi">fatcat:wqgn7munmfb7josi3e2ohqg5pi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921234444/https://dipot.ulb.ac.be/dspace/bitstream/2013/200878/3/1502.07405v1.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/8c/fd/8cfde3070ec24dcf889f4d862cc439cc97b75638.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/15m1010117"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling [article]

Pieter Ghysels, Xiaoye S. Li, Francois-Henry Rouet, Samuel Williams, Artem Napov
<span title="2015-02-25">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices.  ...  We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices.  ...  Yvan Notay provided the code to generate the convection diffusion matrices and the code for the Helmholtz problems was provided by Shen Wang.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.07405v1">arXiv:1502.07405v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oomyoy5um5dmtm6ceifrfusgpy">fatcat:oomyoy5um5dmtm6ceifrfusgpy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191016193921/https://arxiv.org/pdf/1502.07405v1.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/21/65/2165f5fe2c98e528a92c7bf9d29bcf5180dc2226.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.07405v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

An iterative working-set method for large-scale nonconvex quadratic programming

Nicholas I.M. Gould, Philippe L. Toint
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4noeh234gba3bhigjkwuibtn3u" style="color: black;">Applied Numerical Mathematics</a> </i> &nbsp;
Details of an implementation-the Fortran 90 package QPA in the forthcoming GALAHAD library-are given.  ...  The methods are iterative at two levels, one level relating to the selection of the current working set, and the second due to the method used to solve the equality-constrained problem for this working  ...  An alternative is to "undo" the previous addition by removing the row and column from S corresponding to the outgoing constituent row ( a T A 0 0 0 0).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0168-9274(02)00120-4">doi:10.1016/s0168-9274(02)00120-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dq6m7xqc7ndarjjtiiihhbdvge">fatcat:dq6m7xqc7ndarjjtiiihhbdvge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809010540/http://www.numerical.rl.ac.uk/people/nimg/pubs/GoulToin02_appnummath.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/ab/db/abdb8316f14e440391910025eccac38df1640617.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0168-9274(02)00120-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods

G. W. S., Richard Barrett, Michael Berry, Tony F. Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, Henk van der Vorst
<span title="">1995</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
methods, multigrid-like methods, and row-projection schemes.  ...  In this chapter we present both historical development and state-of-the-art methods for solving some of the most challenging computational problems facing researchers.  ...  We also thank Geoffrey Fox for initial discussions on the concept of templates, and Karin Remington for designing the front cover.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2153507">doi:10.2307/2153507</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yumeh4c3fnhg3iuxnl2ohkn3wa">fatcat:yumeh4c3fnhg3iuxnl2ohkn3wa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811225833/http://www.cfm.brown.edu/faculty/gk/AM258/Handouts/templates.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/e4/49/e449cb8b5c582e435a1c015de9de936b14a3b509.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2153507"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> jstor.org </button> </a>

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

A Marek, V Blum, R Johanni, V Havu, B Lang, T Auckenthaler, A Heinecke, H-J Bungartz, H Lederer
<span title="2014-05-02">2014</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yojdv2w2kvbhpfrlimnuijuoza" style="color: black;">Journal of Physics: Condensed Matter</a> </i> &nbsp;
ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel  ...  The computational effort formally scales as O(N 3 ) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that  ...  V H acknowledges the computer time provided by CSCthe Finnish IT Center for Science.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/0953-8984/26/21/213201">doi:10.1088/0953-8984/26/21/213201</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24786764">pmid:24786764</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kagmuswa4nd43ioehd3ughhid4">fatcat:kagmuswa4nd43ioehd3ughhid4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808192754/https://th.fhi-berlin.mpg.de/site/uploads/Publications/JPCM-26-213201-2014.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/aa/12/aa12cf8052a7d83fed5e0a7d7c374ac2edad21d4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/0953-8984/26/21/213201"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> iop.org </button> </a>

Gaussian elimination for the solution of linear systems of equations [chapter]

Gérard Meurant
<span title="">2000</span> <i title="Elsevier"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eayr6uw6l5aojipnbm5smbbeby" style="color: black;">Handbook of Numerical Analysis</a> </i> &nbsp;
Today, it is well known and recognized that there are much better methods than Cramer's rule which is almost never used for solving linear systems.  ...  The well known linear algebra package LINPACK (for linear systems solves and least square problems) was written using BLAS1 and published in 1979 (Bunch, Dongarra, Moler and Stewart [1979] ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1570-8659(00)07002-2">doi:10.1016/s1570-8659(00)07002-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bh4sujyd4fbsxdtdujvwwo4nbe">fatcat:bh4sujyd4fbsxdtdujvwwo4nbe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809044349/http://gerard.meurant.pagesperso-orange.fr/handbook_2000.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/0f/83/0f835dc75b72a772a55d8324470094e548711e30.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1570-8659(00)07002-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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