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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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.

 

Theoretical analysis of Sinc-Nyström methods for Volterra integral equations
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by Tomoaki Okayama, Takayasu Matsuo and Masaaki Sugihara PDF
Math. Comp. 84 (2015), 1189-1215 Request permission

Abstract:

In this paper, we present three theoretical results on Sinc-Nyström methods for Volterra integral equations of the first and second kind, which were proposed by Muhammad et al. Their methods involve the following issues: 1) it is difficult to determine the tuning parameter unless the solution is given, and 2) convergence has not been proved in a precise sense. In a mathematically rigorous manner, we present an implementable way to estimate the tuning parameter and a rigorous proof of the convergence with its rate explicitly revealed. Furthermore, we show that the resulting system is well conditioned. Numerical examples that support the theoretical results are also presented.
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Additional Information
  • Tomoaki Okayama
  • Affiliation: Graduate School of Economics, Hitotsubashi University, 2-1, Naka, Kunitachi, Tokyo, 186-8601, Japan
  • Email: tokayama@econ.hit-u.ac.jp
  • Takayasu Matsuo
  • Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo, 113-8656, Japan
  • MR Author ID: 664782
  • Email: matsuo@mist.i.u-tokyo.ac.jp
  • Masaaki Sugihara
  • Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo, 113-8656, Japan
  • Email: m_sugihara@mist.i.u-tokyo.ac.jp
  • Received by editor(s): March 26, 2013
  • Published electronically: December 30, 2014
  • Additional Notes: The first author was supported by JSPS Grants-in-Aid for Scientific Research.
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 1189-1215
  • MSC (2010): Primary 65R20; Secondary 45D05
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02929-3
  • MathSciNet review: 3315505