Function classes for successful DE-Sinc approximations

Tanaka, Ken’ichiro; Sugihara, Masaaki; Murota, Kazuo

doi:10.1090/S0025-5718-08-02196-0

Function classes for successful DE-Sinc approximations
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by Ken’ichiro Tanaka, Masaaki Sugihara and Kazuo Murota PDF

Math. Comp. 78 (2009), 1553-1571 Request permission

Abstract:

The DE-Sinc formulas, resulting from a combination of the Sinc approximation formula with the double exponential (DE) transformation, provide a highly efficient method for function approximation. In many cases they are more efficient than the SE-Sinc formulas, which are the Sinc approximation formulas combined with the single exponential (SE) transformations. Function classes suited to the SE-Sinc formulas have already been investigated in the literature through rigorous mathematical analysis, whereas this is not the case with the DE-Sinc formulas. This paper identifies function classes suited to the DE-Sinc formulas in a way compatible with the existing theoretical results for the SE-Sinc formulas. Furthermore, we identify alternative function classes for the DE-Sinc formulas, as well as for the SE-Sinc formulas, which are more useful in applications in the sense that the conditions imposed on the functions are easier to verify.

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