Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:A4L-A
Session:
Number:A4L-A1
A Verified Automatic Repeated Integration Algorithm based on Double Exponential Formula
Naoya Yamanaka, Shin’ichi Oishi, Takeshi Ogita,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
The double exponential formula for numerical univariate integration is known to be highly efficient. In this paper we describe an automatic repeated integration algorithm using the double exponential formula for verified computation. Direct product method, which is to regard 2 dimensional repeated integration as an 2-fold iterated integration and apply an univariate quadrature to each variable separately, have been employed for getting integral value. Numerical results are presented showing the performance of the proposed algorithm.