Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:C2L-C
Session:
Number:C2L-C4
Fast Verified Automatic Integration Algorithm using Complex Analysis
Naoya YAMANAKA, Takeshi OGITA, Masahide KASHIWAGI, Shin’ichi OISHI,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
This paper is concerned with verified automatic integration of a univariate function. For this purpose, interval arithmetic and automatic differentiation have widely been used to calculate the error of integral. In this paper, we propose fast verified automatic integration algorithm using an a priori error algorithm for rounding errors in floating-point arithmetic and new algorithm for truncation error which is based on complex analysis. Numerical results are illustrated that proposed verified algorithm is from 5 to 15 times faster than conventional verified method.