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Numerische Mathematik

, Volume 111, Issue 4, pp 631–655 | Cite as

Function classes for double exponential integration formulas

  • Ken’ichiro Tanaka
  • Masaaki SugiharaEmail author
  • Kazuo Murota
  • Masatake Mori
Article

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.

Mathematics Subject Classification (2000)

65D30 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Ken’ichiro Tanaka
    • 1
  • Masaaki Sugihara
    • 1
    Email author
  • Kazuo Murota
    • 1
  • Masatake Mori
    • 2
  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoBunkyo-kuJapan
  2. 2.Department of Mathematical SciencesTokyo Denki UniversityHikiJapan

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