Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Function classes for successful DE-Sinc approximations
HTML articles powered by AMS MathViewer

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.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 65D05, 41A25, 41A30
  • Retrieve articles in all journals with MSC (2000): 65D05, 41A25, 41A30
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
  • 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]
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2501063