Numerical Methods via Transformations

  • Frank Stenger
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)

Abstract

This article begins with the setting of equi-spaced approximation, and then connects these methods with various other numerical methods via simple transformations. In particular, one thus traverses the classes of methods to which Gautschi made many contributions. We also comment on the multistep formulas derived by Gautschi, based on exactness for trigonometric polynomials which deserves further study, owing to its potential power.

Keywords

Sine 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Davis P. J. On the numerical integration of periodic analytic functions. In On Numerical Approximation, pages 303–313. University of Wisconsin Press, Madison, 1953. R. Langer, ed.Google Scholar
  2. [2]
    Gautschi W. Numerical integration of ordinary differential equations based on trigonometric functions. Numer. Math., 3: 381–397, 1961.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Gautschi W. Algorithm 351—Gaussian quadrature formulas. Comm. ACM, 11: 432–436, 1968.CrossRefGoogle Scholar
  4. [4]
    Kowalski M., Sikorski K., Stenger F. Selected Topics In Approximation And Computation. To be published by Oxford University Press, 1994.Google Scholar
  5. [5]
    Lund J., Bowers K. L. Sinc Methods for Quadrature and Differential Equations. SIAM, 1992.CrossRefGoogle Scholar
  6. [6]
    Stenger F. Numerical Methods Based on Sinc and Analytic Functions. Springer-Verlag, N.Y., 1993.MATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • Frank Stenger
    • 1
  1. 1.Department of Computer ScienceUniversity of UtahSalt Lake CityUSA

Personalised recommendations