A fast verified automatic integration algorithm using double exponential formula-Reference-Cited by-同舟云学术

A fast verified automatic integration algorithm using double exponential formula

Published:2010 Issue:1 Volume:1 Page:119-132
ISSN:2185-4106
Container-title:Nonlinear Theory and Its Applications, IEICE
language:en
Short-container-title:NOLTA

Author:

Yamanaka Naoya¹,Okayama Tomoaki²,Oishi Shin'ichi¹³,Ogita Takeshi⁴

Affiliation:

1. Waseda University

2. The University of Tokyo

3. CREST, JST

4. Tokyo Woman's Christian University

Publisher

Institute of Electronics, Information and Communications Engineers (IEICE)

Subject

Rehabilitation,Physical Therapy, Sports Therapy and Rehabilitation,General Medicine

Link

https://www.jstage.jst.go.jp/article/nolta/1/1/1_1_119/_pdf

Reference12 articles.

1. [1] H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,” Publ. RIMS, Kyoto Univ, vol. 9, pp. 721-741, 1974.

2. [2] M. Sugihara, “Optimality of the double exponential formula,” Numerische Mathematik, vol. 75, pp. 379-395, 1997.

3. [3] K. Tanaka, M. Sugihara, K. Murota, and M. Mori, “Function classes for double exponential integration formulas,” Numerische Mathematik, vol. 111, pp. 631-655, 2009.

4. [4] Y. Kobata and N. Yamamoto, “Verified numerical integration using double exponential formula,” Master Thesis, The University of Electro-Communications, 2003.

5. [5] T. Okayama, T. Matsuo, and M. Sugihara, “Error estimates with explicit constants for sinc approximation, sinc quadrature and sinc indefinite integration,” METR2009-01, The university of Tokyo, 2009.

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