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Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities
April 2014
GCC2014
This paper investigates the sufficient conditions for the asymptotic convergence of a generic branch and prune algorithm dedicated to the verified quadrature of a function in several variables. Quadrature over domains defined by inequalities, and adaptive meshing strategies are in the scope of this analysis. The framework is instantiated using certified quadrature methods based on Taylor models (i.e. Taylor approximations with rigorously bounded remainder), and reported experiments confirmed the analysis. They also show that the performances of the instantiated algorithm are comparable with current methods for certified quadrature.
Journal
Alexandre Goldsztejn, Jorge Cruz, Elsa Carvalho
Journal of Computational and Applied Mathematics
Elsevier
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260
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543 - 560
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0377-0427
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http://www.sciencedirect.com/science/article/pii/S0377042713004494
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Alexandre Goldsztejn and Jorge Cruz and Elsa Carvalho, Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities, Journal of Computational and Applied Mathematics, Vol. 260, Pag. 543 - 560, Elsevier, ISSN 0377-0427, (http://www.sciencedirect.com/science/article/pii/S0377042713004494), April 2014.
<b>Alexandre Goldsztejn, <a href="/people/members/view.php?code=3f6f0c9973cdaeab1a3dd815682bb0ac" class="author">Jorge Cruz</a> and <a href="/people/members/view.php?code=8d1b2918d558af8e9308270b485b62a8" class="author">Elsa Carvalho</a></b>, <u>Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities</u>, Journal of Computational and Applied Mathematics, Vol. 260, Pag. 543 - 560, <a href="http://www.elsevier.com/" title="Link to external entity..." target="_blank" class="publisher">Elsevier</a>, ISSN 0377-0427, (<a href="http://www.sciencedirect.com/science/article/pii/S0377042713004494" target="_blank">url</a>), April 2014.
@article {GCC2014, author = {Alexandre Goldsztejn and Jorge Cruz and Elsa Carvalho}, title = {Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities}, journal = {Journal of Computational and Applied Mathematics}, publisher = {Elsevier}, volume = {260}, pages = {543 - 560}, issn = {0377-0427}, url = {http://www.sciencedirect.com/science/article/pii/S0377042713004494}, abstract = {This paper investigates the sufficient conditions for the asymptotic convergence of a generic branch and prune algorithm dedicated to the verified quadrature of a function in several variables. Quadrature over domains defined by inequalities, and adaptive meshing strategies are in the scope of this analysis. The framework is instantiated using certified quadrature methods based on Taylor models (i.e. Taylor approximations with rigorously bounded remainder), and reported experiments confirmed the analysis. They also show that the performances of the instantiated algorithm are comparable with current methods for certified quadrature.}, month = {April}, year = {2014}, }
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