Explicit error bound for modified numerical iterated integration by means of Sinc methods
Numerical Analysis
2022-03-04 v3 Numerical Analysis
Abstract
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit error bound is given in a computable form for the modified formula. The formula works quite efficiently, especially if the integrand is of a product type. Numerical examples that confirm it are also presented.
Cite
@article{arxiv.1306.6615,
title = {Explicit error bound for modified numerical iterated integration by means of Sinc methods},
author = {Tomoaki Okayama},
journal= {arXiv preprint arXiv:1306.6615},
year = {2022}
}
Comments
Keyword: Sinc quadrature, Sinc indefinite integration, repeated integral, verified numerical integration, double-exponential transformation