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Function classes for successful DE-Sinc approximations


Authors: Ken'ichiro Tanaka, Masaaki Sugihara and Kazuo Murota
Journal: Math. Comp. 78 (2009), 1553-1571
MSC (2000): Primary 65D05; Secondary 41A25, 41A30
DOI: https://doi.org/10.1090/S0025-5718-08-02196-0
Published electronically: October 28, 2008
MathSciNet review: 2501063
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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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Additional Information

Ken'ichiro Tanaka
Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

Masaaki Sugihara
Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
Email: m_sugihara@mist.i.u-tokyo.ac.jp

Kazuo Murota
Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
Email: murota@mist.i.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0025-5718-08-02196-0
Keywords: Sinc approximation, double exponential transformation
Received by editor(s): February 8, 2007
Received by editor(s) in revised form: June 19, 2008
Published electronically: October 28, 2008
Additional Notes: This work was supported by the 21st Century COE Program on Information Science and Technology Strategic Core and a Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan. The first author was supported by the Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists. Technical details omitted in this paper can be found in [14]
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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