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Function classes for double exponential integration formulas

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Abstract

The double exponential (DE) formulas for numerical integration are known to be highly efficient, more efficient than the single exponential (SE) formulas in many cases. Function classes suited to the SE formulas have already been investigated in the literature through rigorous mathematical analysis, whereas this is not the case with the DE formulas. This paper identifies function classes suited to the DE formulas in a way compatible with the existing theoretical results for the SE formulas. The DE formulas are good for more restricted classes of functions, but more efficient for such functions. Two concrete examples demonstrate the subtlety in the behavior of the DE formulas that is revealed by our theoretical analysis.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Ken’ichiro Tanaka, Masaaki Sugihara & Kazuo Murota

  2. Department of Mathematical Sciences, Tokyo Denki University, Ishizaka, Hatoyama, Hiki, Saitama, 359-0394, Japan

    Masatake Mori

Authors
  1. Ken’ichiro Tanaka
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  2. Masaaki Sugihara
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  3. Kazuo Murota
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  4. Masatake Mori
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Correspondence to Masaaki Sugihara.

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Tanaka, K., Sugihara, M., Murota, K. et al. Function classes for double exponential integration formulas. Numer. Math. 111, 631–655 (2009). https://doi.org/10.1007/s00211-008-0195-1

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  • DOI: https://doi.org/10.1007/s00211-008-0195-1

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