Romberg extrapolation for Euler summation-based cubature on regular regions

Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in q dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-ba...

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Detalles Bibliográficos
Autores principales: Freeden, W., Gerhards, C.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2017
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5683070/
https://www.ncbi.nlm.nih.gov/pubmed/29177021
http://dx.doi.org/10.1007/s13137-017-0097-4
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author Freeden, W.
Gerhards, C.
author_facet Freeden, W.
Gerhards, C.
author_sort Freeden, W.
collection PubMed
description Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in q dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary q-dimensional regular regions [Formula: see text] and derive an explicit representation for the remainder term.
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spelling pubmed-56830702017-11-22 Romberg extrapolation for Euler summation-based cubature on regular regions Freeden, W. Gerhards, C. GEM Original Paper Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in q dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary q-dimensional regular regions [Formula: see text] and derive an explicit representation for the remainder term. Springer Berlin Heidelberg 2017-09-11 2017 /pmc/articles/PMC5683070/ /pubmed/29177021 http://dx.doi.org/10.1007/s13137-017-0097-4 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Original Paper
Freeden, W.
Gerhards, C.
Romberg extrapolation for Euler summation-based cubature on regular regions
title Romberg extrapolation for Euler summation-based cubature on regular regions
title_full Romberg extrapolation for Euler summation-based cubature on regular regions
title_fullStr Romberg extrapolation for Euler summation-based cubature on regular regions
title_full_unstemmed Romberg extrapolation for Euler summation-based cubature on regular regions
title_short Romberg extrapolation for Euler summation-based cubature on regular regions
title_sort romberg extrapolation for euler summation-based cubature on regular regions
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5683070/
https://www.ncbi.nlm.nih.gov/pubmed/29177021
http://dx.doi.org/10.1007/s13137-017-0097-4
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