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Finite element formulation for modeling nonlinear viscoelastic elastomers

Pedro Areias, Karel Matouš
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gctv3v6plrgwthusala4ydxxeq" style="color: black;">Computer Methods in Applied Mechanics and Engineering</a> </i> &nbsp;
A general second-order unconditionally stable exponential integrator based on a diagonal Padé approximation is developed and the Bergström-Boyce nonlinear viscoelastic law is employed as a prototype model  ...  Finally, several viscoelastic examples, including a study of the unit cell for a solid propellant, are solved to demonstrate the computational algorithm and relevant underlying physics.  ...  Davis serving as program monitors, and from the Center for Simulation of Advanced Rockets (CSAR) under Contract No.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cma.2008.06.015">doi:10.1016/j.cma.2008.06.015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sciax6alnfey7c44g72l7q2vme">fatcat:sciax6alnfey7c44g72l7q2vme</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150501064613/http://www3.nd.edu:80/~kmatous/Papers/CMAME_NonVis.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/db/54/db5463acb8f7d3a9a0add7d41953a1d806e4e07d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cma.2008.06.015"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Feature Extraction using Sparse SVD for Biometric Fusion in Multimodal Authentication

Pavan Kumar K, P. E. S. N. Krishna Prasad, M. V. Ramakrishna, B.D.C.N. Prasad
<span title="2013-07-31">2013</span> <i title="Academy and Industry Research Collaboration Center (AIRCC)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j62rfr7b3rdbdoatlol5nazobq" style="color: black;">International journal of network security and its applications</a> </i> &nbsp;
In stage 1, fusion of face and finger patterns using Principal Component Analysis (PCA), in stage 2 by applying Sparse SVD decomposition to extract the feature patterns from the fusion data and face pattern  ...  The exponential of matrix can be computed in various ways such as Taylor Series, Pade Approximation and also using Ordinary Differential Equations (O.D.E.).  ...  FEATURE EXTRACTION USING SPARSE SVD[1] The singular value decomposition, or SVD, is a very powerful and useful matrix decomposition, particularly in the context of data analysis, dimension reducing transformations  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5121/ijnsa.2013.5406">doi:10.5121/ijnsa.2013.5406</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zfzakrdjnnbhjiz6auznhjt2im">fatcat:zfzakrdjnnbhjiz6auznhjt2im</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190728020200/http://airccse.org:80/journal/nsa/5413nsa06.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/67/60/67602bd04df68e3c897586714217b590bf4e8d17.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5121/ijnsa.2013.5406"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Exponential convergence through linear finite element discretization of stratified subdomains

Murthy N. Guddati, Vladimir Druskin, Ali Vaziri Astaneh
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
Named complex-length finite element method (CFEM), the technique is linked to Pade approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified  ...  Exponential convergence facilitates drastic reduction in the number of elements.  ...  DMS-1016514) and Schlumberger Technology Corporation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2016.06.045">doi:10.1016/j.jcp.2016.06.045</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gj33xqmyezf75cuq54subsnu7u">fatcat:gj33xqmyezf75cuq54subsnu7u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180723154148/https://manuscript.elsevier.com/S0021999116302704/pdf/S0021999116302704.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/d3/c5/d3c594513cb89984351ac1ec35913c73267d1890.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2016.06.045"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Matrix exponentials and parallel prefix computation in a quantum control problem

T. Auckenthaler, M. Bader, T. Huckle, A. Spörl, K. Waldherr
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sv4mpg7lmfaqdp24ohp5qqiobm" style="color: black;">Parallel Computing</a> </i> &nbsp;
For the matrix exponential we compare three methods: the eigendecomposition method, the Padé method and a polynomial expansion based on Chebyshev polynomials.  ...  As problem size grows exponentially with the system size, it is necessary to deal with fast numerical algorithms and implementations.  ...  Acknowledgements This work has been performed in the framework of the HLRB 2 Project h1051(see [10] ), Advanced Quantum Control by Gradient-Flow Algorithms on Parallel Clusters at Leibniz Rechenzentrum  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.parco.2010.01.006">doi:10.1016/j.parco.2010.01.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mcmgrw3wkvejrbztiyu33f766y">fatcat:mcmgrw3wkvejrbztiyu33f766y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401173328/http://www5.in.tum.de/persons/huckle/ParCoExpmPrefix.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/89/d0/89d02bbf9eac7055a1054a8ddc8e059b190a5cba.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.parco.2010.01.006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Computation of Kinematic and Magnetic α-Effect and Eddy Diffusivity Tensors by Padé Approximation

Sílvio M.A. Gama, Roman Chertovskih, Vladislav Zheligovsky
<span title="2019-06-14">2019</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bqnhgw7njc53i7otzqblwexk4" style="color: black;">Fluids</a> </i> &nbsp;
We present examples of Padé approximations of the α -effect and eddy viscosity/diffusivity tensors in various flows.  ...  Turning to the kinematic dynamo problem for three-dimensional flows of an incompressible fluid, we explore the application of Padé approximants for the computation of tensors of magnetic α -effect and,  ...  the Padé approximation, M and L, by the number of the "missing" dimensions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/fluids4020110">doi:10.3390/fluids4020110</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cdwypljcwrhwxkehdtfd3bdooy">fatcat:cdwypljcwrhwxkehdtfd3bdooy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200207221640/https://res.mdpi.com/d_attachment/fluids/fluids-04-00110/article_deploy/fluids-04-00110-v2.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/56/ab/56ab49a980744c581121b86b85baa6ead6cbe91e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/fluids4020110"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

Vladimir Kazeev, Mustafa Khammash, Michael Nip, Christoph Schwab, Daniel A. Beard
<span title="2014-03-13">2014</span> <i title="Public Library of Science (PLoS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ch57atmlprauhhbqdf7x4ytejm" style="color: black;">PLoS Computational Biology</a> </i> &nbsp;
, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions.  ...  The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sublinearly in the mode size (maximum copy number),  ...  The method uses the Arnoldi iteration to compute the Krylov subspace up to some order of accuracy then computes the matrix exponential in that smaller space (by diagonal Padé approximation).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pcbi.1003359">doi:10.1371/journal.pcbi.1003359</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24626049">pmid:24626049</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3953644/">pmcid:PMC3953644</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tpoxs5tcurgpxobbd5kpxp7ksi">fatcat:tpoxs5tcurgpxobbd5kpxp7ksi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427125442/https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/85098/journal.pcbi.1003359.PDF;jsessionid=D2E5456407C12E3E8AEF4C5AAD222EA9?sequence=2" 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/7a/af/7aaf122a649ecd1f37677bcf0b303498c4095a22.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pcbi.1003359"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> plos.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3953644" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

SANM: A Symbolic Asymptotic Numerical Solver with Applications in Mesh Deformation [article]

Kai Jia
<span title="2021-05-18">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
SANM also extends ANM to support many nonquadratic operators, including intricate ones such as singular value decomposition. Furthermore, SANM generalizes ANM to support the implicit homotopy form.  ...  While we demonstrate on mesh deformation problems, SANM is generic and potentially applicable to many tasks.  ...  We would also like to thank Changxi Zheng, Wojciech Matusik, Liang Shi, and Martin Rinard for the helpful technical discussions and Lingxiao Li for proofreading.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.08535v1">arXiv:2105.08535v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nggtaz5525amnpgqfjudvu765e">fatcat:nggtaz5525amnpgqfjudvu765e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210520042339/https://arxiv.org/pdf/2105.08535v1.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/14/90/149044bc6069030e9bd90c1915b0c41b707cdfac.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.08535v1" 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 exponential integrator for advection-dominated reactive transport in heterogeneous porous media

A. Tambue, G.J. Lord, S. Geiger
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
flows. 82 The aim of this paper is to investigate the exponential time differencing 83 method of order one (ETD1) and compare its performance in terms of ef-84 ficiency and accuracy to standard semi-implicit  ...  In contrast to previous work, we consider heterogeneous media, 80 the exponential time differencing method of order one with the finite volume 81 discretisation in space and examine high Péclet number  ...  Berland 58 et al. [33] used a Padé approximation to compute the matrix exponential 59 of ϕ-functions and provided a package for exponential integrators which is 60 efficient in one dimension. 61 Although  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2010.01.037">doi:10.1016/j.jcp.2010.01.037</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rh32cotefvb4lkk5ylq5yzen7y">fatcat:rh32cotefvb4lkk5ylq5yzen7y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808204902/http://www.macs.hw.ac.uk/~gabriel/Research/TLG.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/fc/83/fc83845302dadd866fb37755f6852bc0047629ba.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2010.01.037"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Generation of transparent boundary conditions for modeling wave propagation in anisotropic media

Nikolay Albertovich Zaitsev, Ivan Lvovich Sofronov
<span title="">2018</span> <i title="Keldysh Institute of Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/75ykmoxkuja6xfu6kz7bwrg23y" style="color: black;">Keldysh Institute Preprints</a> </i> &nbsp;
Sofronov Generation of transparent boundary conditions for modeling wave propagation in anisotropic media The preprint contains results on development of mathematical foundations and numerical approaches  ...  A two-dimensional wave propagation problem in polar coordinates (r, θ) is considered.  ...  An exponential grid is used in the radial direction, shifted for half spacing from the boundaries: Three-point central finite differences in radial direction are used to approximate governing equations  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.20948/prepr-2018-82-e">doi:10.20948/prepr-2018-82-e</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xyk43uef55dstgfowcudzar6yq">fatcat:xyk43uef55dstgfowcudzar6yq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501172643/http://keldysh.ru/papers/2018/prep2018_82_eng.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/9f/09/9f0916dd3018560aa71db49c0d498b5f3be3dbf7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.20948/prepr-2018-82-e"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A μ-mode BLAS approach for multidimensional tensor-structured problems [article]

Marco Caliari, Fabio Cassini, Franco Zivcovich
<span title="2022-05-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present numerical results on experiments up to dimension six from different fields of numerical analysis, which show the effectiveness of the approach.  ...  In this manuscript, we present a common tensor framework which can be used to generalize one-dimensional numerical tasks to arbitrary dimension d by means of tensor product formulas.  ...  Franco Zivcovich has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 850941).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.11238v2">arXiv:2112.11238v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rybsyknw7zc6xgbttcxzby5wqi">fatcat:rybsyknw7zc6xgbttcxzby5wqi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220525184051/https://arxiv.org/pdf/2112.11238v2.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/45/ff/45ffbc0b3558f3400fda95a1d96dd15b32d7a272.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.11238v2" 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>

A μ-mode integrator for solving evolution equations in Kronecker form [article]

Marco Caliari, Fabio Cassini, Lukas Einkemmer, Alexander Ostermann, Franco Zivcovich
<span title="2021-09-23">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also discuss how to efficiently implement this integrator on both multi-core CPUs and GPUs.  ...  The integrator is based on a d-dimensional splitting approach and uses exact (usually precomputed) one-dimensional matrix exponentials.  ...  Acknowledgments The authors would like to thank the Italian Ministry of Instruction, University and Research (MIUR) for supporting this research with funds coming from PRIN Project 2017  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.01691v2">arXiv:2103.01691v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3q6bg4g4uvgzrckmpplxrn4nzm">fatcat:3q6bg4g4uvgzrckmpplxrn4nzm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210304001217/https://arxiv.org/pdf/2103.01691v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7e/ed/7eedd31e8e0fbdf5e6003f587df7fcc974795dfd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.01691v2" 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>

Stochastic analysis of dead-time systems using a hybrid spectral method

Pham Luu Trung Duong, Moonyong Lee
<span title="2015-07-14">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oeafm75vpzfbtmpxwsotjqu3hy" style="color: black;">International Journal of Control, Automation and Systems</a> </i> &nbsp;
Control systems often operate in the presence of dead-time. However, in most works, these dead-time systems are studied in a deterministic manner, which have low precision and reliability.  ...  Many natural systems often suffer stochastic noise that causes fluctuations in their behavior, making their responses deviate from nominal models.  ...  A (3/3) Pade approximation was used in this example. Higher order expansion will not lead to any improvement [20] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s12555-013-0468-z">doi:10.1007/s12555-013-0468-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wdtzpgl43jc35g6wg3tg6gwjgi">fatcat:wdtzpgl43jc35g6wg3tg6gwjgi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160923204825/http://orbilu.uni.lu/bitstream/10993/23693/1/ijcas.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/3c/38/3c38d94fa6dafc0062974160b4b9bd0fc3a70a74.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s12555-013-0468-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

projUNN: efficient method for training deep networks with unitary matrices [article]

Bobak Kiani, Randall Balestriero, Yann Lecun, Seth Lloyd
<span title="2022-03-11">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We propose instead an efficient method based on rank-k updates – or their rank-k approximation – that maintains performance at a nearly optimal training runtime.  ...  Even in the fastest setting (k=1), projUNN is able to train a model's unitary parameters to reach comparable performances against baseline implementations.  ...  [HWY18] and [SF21] employ approximations to the matrix exponential via Padé or Taylor series approximations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2203.05483v2">arXiv:2203.05483v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p7yafy4iczdzhhw7o7j5u4n4vq">fatcat:p7yafy4iczdzhhw7o7j5u4n4vq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220323025252/https://arxiv.org/pdf/2203.05483v2.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/e7/e2/e7e2379df7247de1484ed31bffcdbcd5396d627c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2203.05483v2" 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>

Quantum phase diagram and excitations for the one-dimensionalS=1Heisenberg antiferromagnet with single-ion anisotropy

A. Fabricio Albuquerque, Chris J. Hamer, Jaan Oitmaa
<span title="2009-02-11">2009</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lqjgbsoa65gghi2p2esulcqqqm" style="color: black;">Physical Review B</a> </i> &nbsp;
By employing high-order series expansions and quantum Monte Carlo simulations we obtain accurate estimates for the critical points separating different phases in the quantum phase diagram.  ...  Additionally, excitation spectra and gaps are obtained.  ...  Laflorencie and M. Troyer. This work has been supported by the Australian Research Council.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevb.79.054412">doi:10.1103/physrevb.79.054412</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/amsg6ngdebgubmtrk6iwcljzlu">fatcat:amsg6ngdebgubmtrk6iwcljzlu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191019160311/https://arxiv.org/pdf/0811.0646v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/4d/164d06eccb42c93252c20848e64517c6dfb16cd9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevb.79.054412"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Implementation of harmonic balance reduced model order equation

Abdallah Hijazi, Sebastien Mons, Edouard Ngoya
<span title="">2012</span> <i title="IEEE"> 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-wave Circuits </i> &nbsp;
Bernard Jarry, head of department, for receiving me in his team. I would like to express my sincere gratitude to my advisor Prof.  ...  His guidance helped me in all the time of research and writing of this thesis. I would like to thank the rest of my thesis committee: M. Juan-Mari COLLANTES, Mme Almudena SUAREZ, M.  ...  -17 and ( ) ( ) II-18 As shown from the above analysis, finding the solution at each time step requires several LU decompositions of the Jacobian matrix in order to solve the linear system of equations  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/inmmic.2012.6331952">doi:10.1109/inmmic.2012.6331952</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l3hm4ipgsnb2lptqekxxiejpee">fatcat:l3hm4ipgsnb2lptqekxxiejpee</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200710032741/https://tel.archives-ouvertes.fr/tel-01614852/document" 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/fd/4e/fd4e9c256a1f79e17b20aebb6fe22aef76a17650.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/inmmic.2012.6331952"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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