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<identifier>oai:HAL:hal-00730194v1</identifier>
<datestamp>2018-01-11</datestamp>
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<setSpec>subject:math</setSpec>
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<setSpec>collection:INRIA-LILLE</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Differential equations and solution of linear systems</title>
<creator>Laminie, Jacques</creator>
<creator>Chehab, Jean-Paul</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>SImulations and Modeling for PArticles and Fluids (SIMPAF) ; Laboratoire Paul Painlevé - UMR 8524 (LPP) ; Université de Lille, Sciences et Technologies - Centre National de la Recherche Scientifique (CNRS) - Université de Lille, Sciences et Technologies - Centre National de la Recherche Scientifique (CNRS) - Inria Lille - Nord Europe ; Institut National de Recherche en Informatique et en Automatique (Inria) - Institut National de Recherche en Informatique et en Automatique (Inria)</contributor>
<description>International audience</description>
<source>ISSN: 1017-1398</source>
<source>EISSN: 1572-9265</source>
<source>Numerical Algorithms</source>
<publisher>Springer Verlag</publisher>
<identifier>hal-00730194</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00730194</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00730194</source>
<source>Numerical Algorithms, Springer Verlag, 2005, 40 (2), pp.103-124</source>
<language>en</language>
<subject>[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical methods in numerical linear algebra by modelling the linear system to be solved as a given state of a dynamical system; the solution can be reached asymptotically, as a (asymptotically stable) steady state, but also as a finite time (shooting methods). In that way, any (stable) numerical scheme for the integration of such a problem can be presented as a method for solving linear systems. The authors discuss aspects of this approach, which allows them to recover some known methods but also to introduce new ones. Finally, some convergence results and numerical illustrations are presented.</description>
<date>2005</date>
</dc>
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