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A Fast Automatic Integration Algorithm using Double Exponential Formula based on Verification Theory
Naoya Yamanaka,Tomoaki Okayama,Shin’ichi Oishi,Takeshi Ogita 대한전자공학회 2009 ITC-CSCC :International Technical Conference on Ci Vol.2009 No.7
A fast automatic integration algorithm of calculating univariate integrals over finite interval using numerical computations is proposed. The proposed algorithm is based on the double exponential formula. In order that the formula works accurately and efficiently, we have presented a theorem for verified computations. In this paper, we propose an approximate integration algorithm based on this theorem. Numerical results are presented showing the performance of the proposed algorithm.