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A Note on the Extended Rosenbrock Function

Yun-Wei Shang, Yu-Huang Qiu
<span title="2006-03-01">2006</span> <i title="MIT Press - Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b7u6fu546fgplmudjzcn5zqqme" style="color: black;">Evolutionary Computation</a> </i> &nbsp;
The classical Rosenbrock function, which is a two-dimensional unimodal function, has been extended to higher dimensions in recent years.  ...  In addition, this paper demonstrates that one of the "local minima" for the 20-variable Rosenbrock function found by Deb might not in fact be a local minimum.  ...  Acknowledgments This material is based on research supported by Chinese National Science Foundation Grant 60075018.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/106365606776022733">doi:10.1162/106365606776022733</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/16536893">pmid:16536893</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dxqz4jsxp5fahi7a6hkf4gh6o4">fatcat:dxqz4jsxp5fahi7a6hkf4gh6o4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211015230109/https://watermark.silverchair.com/evco.2006.14.1.119.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAtMwggLPBgkqhkiG9w0BBwagggLAMIICvAIBADCCArUGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMfiAQapRdcJWwuAPKAgEQgIIChpDHVD6_SXN0rKrT3jWDjAI1pXq5kBfo53L3NEeZ0lEi1dNnqeKCHUiywKE4tiseApC5BU2qhWLaMM_7XPvULk019yGiHyxj6WVSh8BlqMO9Xc6oVqkCa8XrzwADmjJzkvUEOO-vO43VAh-RCqDbOFrcICFDc5T0tT4cCGASoFM1N_5R8J5MQUKhZKzVxwUlzCuU_2k9d1zet39yi_1nlZiioOnN8mUv0ZCdcrhWF16bChSwTjl046BhDXegvHv2zpxoFZbBwi34bLUfM7TaIdFkz49lzGiqC7DQGxxb_7oOov9UvxRcY5ldRcT6pEnn6ehlFhRRLsKx6Phu0lBplBOzpxld9hZnU498VUkqzX7JxilUeyRJ2XvvXr2xOFzEjzIYSarF2JZ-X9GTdR1Xc4lrWXI_N04evNpgXpO2yzttRDQHw1OjUjTXO4tp60qYhF7rvD1EhQMULlmCJe6o_AKaad4nGFrVCq58KDo0HUvotRlI2vWrVrLx_BVr4EgFIuxrkdzlbAG7BdHrwuYTIMhqKMHYn8JavymMftv7CyjXrDVFaDEh7uy0kA-2YAF2Aa9Km0AqA4SVbZtsLtkUKkm8QKGFrJlc6KHtpqhQNG1q-Dl4lDMpe2mG5U143K61fRkoLtdQ-kBv06DL-2WtzvBniTYuStByu0EhMqp5_x-mYQMGiWP-J1vDPopQ3DFhpfUGyQOcRuSJqQYfTKbHB2RYXzGYGQMUdO8shHVJpq02cQaix2LEgj4OUM8QNCXTAR5U_-Suo9rcHb2Uty6LfZJci95HUzJXdyiKhLrt9tG75GU-zW4ywcc7rceaATkTCAtVpm_JaB-MEyy1Xk5Oim-2c1nUKj0" 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/f4/f6/f4f69254569c7261a366f1945a40af533e385b32.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/106365606776022733"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> mitpressjournals.org </button> </a>

A Note on the Extended Rosenbrock Function

Yun-Wei Shang, Yu-Huang Qiu
<span title="">2006</span> <i title="MIT Press - Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b7u6fu546fgplmudjzcn5zqqme" style="color: black;">Evolutionary Computation</a> </i> &nbsp;
The classical Rosenbrock function, which is a two-dimensional unimodal function, has been extended to higher dimensions in recent years.  ...  In addition, this paper demonstrates that one of the "local minima" for the 20-variable Rosenbrock function found by Deb might not in fact be a local minimum.  ...  Acknowledgments This material is based on research supported by Chinese National Science Foundation Grant 60075018.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/evco.2006.14.1.119">doi:10.1162/evco.2006.14.1.119</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/16536893">pmid:16536893</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6tcb6zaoarbnjnlesigbtiuep4">fatcat:6tcb6zaoarbnjnlesigbtiuep4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211014160326/https://watermark.silverchair.com/evco.2006.14.1.119.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAtMwggLPBgkqhkiG9w0BBwagggLAMIICvAIBADCCArUGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMFj0UghMP6R0bTHhuAgEQgIIChv0XKdjk22P3gcQua9w1bElI8wC2SDXE-tfkce5GmhB7IVZu0sF4W4PLGodzJFyO9X7wte_fhooJZSZxuCo6YlWJSTmiUuQFev3Vdu7zDaLl3BLLffPJ5IzlIaxlD2ImLKaNBE81ArWHMizRf9K19wbX8RMlO-YScyHnBB0RLEVEP9RTHACM9VWnH9orPrsZStqpZ0Mv-T0fC7xSwU5UmGyzA2hnnl92TOGSvGkxO6N-fCJuXk-O0rYYySGw9233opvacaf0LjiK20n87Ypb1dzyu67H50bWf3FErY_BmyyTz2SW5Q8_ilMijsv2KXlxT0_DS2qR4Jes7Ap7h53p4Afu_MNpqPnvc8IybjF7p1SIsuZ6LmWJp78Ov-wBVst7qnRvoQ5C92UcZQc7cSw-f-o-cdLSke9hrESh64zBnfgbZl9JVmlV3zY9tMeoQ_tLWD-Pmyh1LtYVWJK1vcGrNEg6d9nbw3zehK98HFc4zacIHi1cCXaPRRcgHdZjxxKPp88AH9UzVeIIbfjwskpqRaSYbxu6AGHP0syZK-MADaiJZPZaeegptoT36ZaTbKY6g-zhNhS1jXKdAmaIXOj8yb8QWli_aKLfptj1HuJuLWh-Blh8Bufopjy_V8Vh0IMywH9caVgb23Ue3T9YKbT4JOBM1nxlY8GyWsBvwVuC46FRe8zp8uUBT4GXrw8GOk0WBKMms0VQ4_4YDobcpvl6r4Iz4NTMmdKxnWbbm0G4RAH02C64wfwFyRJK-ArvzHr-1Dvxqf2UKNcnUOeXSuKTBSJyDUE00hs9X1XplsEGc1l_9npZCyxQEkDyMYQLAi2qmFxuK6PSTiBnNLkRbUT4RG2iQqHZ-PI" 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/76/66/7666550a00c85a013048baed737592266a707bde.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/evco.2006.14.1.119"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> mitpressjournals.org </button> </a>

Page 1435 of Mathematical Reviews Vol. 58, Issue 2 [page]

<span title="">1979</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Regarding the’ minor errors pointed out by Rosenbrock, the authors note that the matter has been rectified in the note of the first author and I. Postlethwaite [Internat. J.  ...  Author’s summary: “The author presents a design procedure for single-loop sampled feedback systems in which the plant transfer function has prescribed bounds on its parameters.  ... 
<span class="external-identifiers"> </span>
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A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation

Wenyuan Liao
<span title="">2015</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dgcr32e3abazpn7i4ocwedp3fa" style="color: black;">Abstract and Applied Analysis</a> </i> &nbsp;
Moreover, it has been shown that the Rosenbrock method is strongly A-stable hence suitable for the stiff ODE system obtained from compact finite difference discretization of the nonlinear parabolic partial  ...  In this work we construct a new fourth-order Rosenbrock method to solve the nonlinear parabolic partial differential equation supplemented with Dirichlet or Neumann boundary condition.  ...  The author gratefully acknowledges the financial support from NSERC.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/539652">doi:10.1155/2015/539652</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h6dnhb6cczduzkxg2i7la6g5hu">fatcat:h6dnhb6cczduzkxg2i7la6g5hu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200215084530/http://downloads.hindawi.com/journals/aaa/2015/539652.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/cc/37/cc37f2db546a948cce5bf1dd77a17fefb14fddc2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/539652"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Research on system zeros: a survey

CHERYL B. SCHRADER, MICHAEL K. SAIN
<span title="">1989</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r467vnh32bfzre7lj4uj5cyv4a" style="color: black;">International Journal of Control</a> </i> &nbsp;
This report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989.  ...  Transmission, invariant, system, module, infinite, and finite zeros are addressed, the latter subdivided into a hierarchical structure with respect to information considered in the definition process.  ...  One common extension of the SISO case is to consider each element of a transfer function matrix G(s) to be an individual transfer function between a certain input and a certain output.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207178908953438">doi:10.1080/00207178908953438</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yyxnm57n6fg6xjd7xoyfhq22xm">fatcat:yyxnm57n6fg6xjd7xoyfhq22xm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20040326215437/http://www.nd.edu:80/~stpaul/education/papers/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/da/93/da93e876c045a46bfb2d630ab79f6a29a5c9b256.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207178908953438"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Implementation and verification of global optimization benchmark problems

Mikhail Posypkin, Alexander Usov
<span title="2017-12-29">2017</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rf3iutrnt5amlkzxv4mzhulade" style="color: black;">Open Engineering</a> </i> &nbsp;
The library automate the process of generating the value of a function and its' gradient at a given point and the interval estimates of a function and its' gradient on a given box using a single description  ...  Based on this functionality, we have developed a collection of tests for an automatic verification of the proposed benchmarks.  ...  Rosenbrock function depicted at the Figure 1 returns an object representing a mathematical expression to the calling code. Note that the function description is specified once.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/eng-2017-0050">doi:10.1515/eng-2017-0050</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hqxnvvcfdja4do5s6en4dw2bqe">fatcat:hqxnvvcfdja4do5s6en4dw2bqe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201202183209/https://www.degruyter.com/downloadpdf/journals/eng/7/1/article-p470.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/5c/96/5c967226c7e65998f487b4982dab925c171f7c2e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/eng-2017-0050"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> degruyter.com </button> </a>

Adaptive Krylov-Type Time Integration Methods [article]

Paul Tranquilli, Ross Glandon, Adrian Sandu
<span title="2019-10-06">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Two approaches for improving the stability and efficiency of Rosenbrock-Krylov methods are proposed, one through direct control of linear system residuals and the second through a novel extension of the  ...  The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage  ...  Acknowledgements This work has been supported in part by NSF through awards NSF DMS1419003 and NSF CCF1613905, AFOSR through the award AFOSR DDDAS 15RT1037, and by the Computational Science Laboratory  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.02514v1">arXiv:1910.02514v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d4r4nykh4fbwrmqfagm3uik4aa">fatcat:d4r4nykh4fbwrmqfagm3uik4aa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831151253/https://arxiv.org/pdf/1910.02514v1.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/23/f4/23f4523130060a5ade14e9f1b0ad4f9971d7a4fc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.02514v1" 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 n ‐dimensional Rosenbrock distribution for Markov chain Monte Carlo testing

Filippo Pagani, Martin Wiegand, Saralees Nadarajah
<span title="2021-05-12">2021</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/occ3rnqmirbpvpgzpjqr6rzacq" style="color: black;">Scandinavian Journal of Statistics</a> </i> &nbsp;
The Rosenbrock function is a ubiquitous benchmark problem in numerical optimization, and variants have been proposed to test the performance of Markov chain Monte Carlo algorithms on distributions with  ...  The Hybrid Rosenbrock distribution is composed of conditional normal kernels arranged in such a way that preserves the key features of the original Rosenbrock kernel.  ...  Our choice is based on the historical importance of the Rosenbrock function, and on the fact that "banana"-like distributions are common in many fields of knowledge.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/sjos.12532">doi:10.1111/sjos.12532</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a5posvrw7vck3og5yyykvse4ny">fatcat:a5posvrw7vck3og5yyykvse4ny</a> </span>
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Rosenbrock--Krylov Methods for Large Systems of Differential Equations

Paul Tranquilli, Adrian Sandu
<span title="">2014</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 paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems.  ...  The time discretization and the Krylov space approximation are treated as a single computational process, and the Krylov space properties are an integral part of the new Rosenbrock-K order condition theory  ...  This work has been supported in part by NSF through awards NSF OCI-8670904397, NSF CCF-0916493, NSF DMS-0915047, NSF CMMI-1130667, NSF CCF-1218454, AFOSR FA9550-12-1-0293-DEF, AFOSR 12-2640-06, and by the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/130923336">doi:10.1137/130923336</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sbfhikayqrgqjasjfa5nk25th4">fatcat:sbfhikayqrgqjasjfa5nk25th4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200827133005/https://arxiv.org/pdf/1305.5481v1.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/0f/db/0fdbf7707415df08176561d96bded4a7158cc3bb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/130923336"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Particle Swarm Optimization with Distance Based Repulsivity

Michal Pluhacek, Ivan Zelinka, Roman Senkerik, Adam Viktorin, Tomas Kadavy
<span title="2018-12-21">2018</span> <i title="Brno University of Technology"> MENDEL </i> &nbsp;
The repulsive mechanism is further extended with a distance-based modification. The results are presented and tested for statistical significance.  ...  In this study, we propose a repulsive mechanism for the Particle Swarm Optimization algorithm that improves its performance on multi-modal problems.  ...  It seems that the variant noted as PSO Repuls. 2 is balanced for use on any shape of the fitness landscape.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13164/mendel.2018.2.081">doi:10.13164/mendel.2018.2.081</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gdo6jvpvjzavvlzumpyyhibh5i">fatcat:gdo6jvpvjzavvlzumpyyhibh5i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321031453/https://mendel-journal.org/index.php/mendel/article/download/21/16" 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/f1/d3f1c9eb9535bcdc971d0879aee126812f141986.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13164/mendel.2018.2.081"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An n-dimensional Rosenbrock Distribution for MCMC Testing [article]

Filippo Pagani, Martin Wiegand, Saralees Nadarajah
<span title="2020-05-07">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The Rosenbrock function is an ubiquitous benchmark problem for numerical optimisation, and variants have been proposed to test the performance of Markov Chain Monte Carlo algorithms.  ...  We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which is composed of conditional normal kernels arranged in such a way that preserves the key features  ...  Simon Cotter for their many useful comments, and the Department of Mathematics at the University of Manchester for PhD funding.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.09556v4">arXiv:1903.09556v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pewrqzxtm5clra7euzek5zr6py">fatcat:pewrqzxtm5clra7euzek5zr6py</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200509010454/https://arxiv.org/pdf/1903.09556v4.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] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.09556v4" 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>

Benchmarking stiff ode solvers for atmospheric chemistry problems II: Rosenbrock solvers

A. Sandu, J.G. Verwer, J.G. Blom, E.J. Spee, G.R. Carmichael, F.A. Potra
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6564ouf3evhmfnxrs43zg7scgi" style="color: black;">Atmospheric Environment</a> </i> &nbsp;
Math., No. 85) and compare eight solvers on a set of seven box-models used in present day models. The focus is on Rosenbrock solvers.  ...  In the numerical simulation of atmospheric transport-chemistry processes, a major task is the integration of the stiff systems of ordinary differential equations describing the chemical transformations  ...  This difference term reveals a dependence of e •. r1 on e .. For a proper functioning of the Rosenbrock method it is desirable that, in an appropriate norm 1111. 11 E(e. + y(t.)) -E(y(r..)) II ~ II£.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1352-2310(97)83212-8">doi:10.1016/s1352-2310(97)83212-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gov5e3wj2bfldcf5qth4az3sv4">fatcat:gov5e3wj2bfldcf5qth4az3sv4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720201422/https://ir.cwi.nl/pub/125/0125D.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/82/54/825425b23912b7f4890c53a07aed2f1af25c6bf3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1352-2310(97)83212-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Linearly implicit GARK schemes [article]

Adrian Sandu, Michael Günther, Steven Roberts
<span title="2020-10-11">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper constructs the new GARK-ROS/GARK-ROW families of multimethods based on linearly implicit Rosenbrock/Rosenbrock-W schemes.  ...  The authors developed the general-structure additive Runge-Kutta (GARK) framework, which constructs multimethods based on Runge-Kutta schemes.  ...  The work of Sandu  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.01612v2">arXiv:2008.01612v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vaiv6fz2d5ewdk2v6jmfspvwri">fatcat:vaiv6fz2d5ewdk2v6jmfspvwri</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201120214210/https://arxiv.org/pdf/2008.01612v2.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/a5/84/a5841277c564d4f1ebe87182efed5d568e4a692b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.01612v2" 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 Enhanced Aggregation Pheromone System for Real-Parameter Optimization in the ACO Metaphor [chapter]

Shigeyoshi Tsutsui
<span title="">2006</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;
The APS replaces pheromone trails in traditional ACO with aggregation pheromones. The pheromone update rule is applied in a way similar to that of ACO.  ...  It allows a stronger exploitation of better solutions found and at the same time it can prevent premature stagnation of the search. Experimental results showed eAPS has higher performance than APS.  ...  Acknowledgements The author would like to acknowledge Dr. Marco Dorigo, the research director of the IRIDIA Lab. at the Université Libre de Bruxelles, for his advice on improving APS.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11839088_6">doi:10.1007/11839088_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jtybck7k4ff6zpbegcidrqcjjq">fatcat:jtybck7k4ff6zpbegcidrqcjjq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120123123834/http://www2.hannan-u.ac.jp/~tsutsui/ps/ants2006.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/4b/5b/4b5bdb4fafce30569f79e9a7aba27affd60e2576.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11839088_6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Searching minima of an N-dimensional surface: A robust valley following method

W. Quapp
<span title="">2001</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;
The effectiveness of the algorithm is demonstrated by using a polynomial test, the notorious Rosenbrock function in two, 20, and in 100 dimensions.  ...  A procedure is proposed to follow the "minimum path" of a hypersurface starting anywhere in the catchment region of the corresponding minimum.  ...  PERFORMANCE Rosenbrock Function, Dimension n = 20 We test TASC with the high dimensional, extended Rosenbrock function in a version where all dimensions are coupled [26] n-1 i=l As well as in the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0898-1221(00)00283-2">doi:10.1016/s0898-1221(00)00283-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hee4p7avgjej5an34hf73edep4">fatcat:hee4p7avgjej5an34hf73edep4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808235947/http://www.mathematik.uni-leipzig.de/~quapp/WQ_CompMAppl.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/f1/f2/f1f29aa5662d87f0031e2f2f0d6e7db48b307958.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0898-1221(00)00283-2"> <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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