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Numerical Algorithms

, Volume 45, Issue 1–4, pp 101–112 | Cite as

An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes

  • Takemitsu Hasegawa
  • Susumu Hibino
  • Yohsuke Hosoda
  • Ichizo Ninomiya
Original Paper

Abstract

An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980) of adaptive type based on the Newton–Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971).

Keywords

Automatic quadrature Adaptive algorithm Numerical comparison 

Mathematics Subject Classifications (2000)

65D30 65D32 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Takemitsu Hasegawa
    • 1
  • Susumu Hibino
    • 1
  • Yohsuke Hosoda
    • 1
  • Ichizo Ninomiya
    • 1
  1. 1.Department of Information ScienceUniversity of FukuiFukuiJapan

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