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
Descripción
Sumario: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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