Numerical Algorithms

, Volume 28, Issue 1–4, pp 63–86

Expansions over a Simplex of Real Functions by Means of Bernoulli Polynomials

  • F. Costabile
  • F. Dell'Accio
Article

Abstract

In [1] there is an expansion in Bernoulli polynomials for sufficiently smooth real functions in an interval [a,b]⊂R that has useful applications to numerical analysis. An analogous result in a 2-dimensional context is derived in [2] in the case of rectangle. In this note we generalize the above-mentioned one-dimensional expansion to the case of Cm-functions on a 2-dimensional simplex; a method to generalize the expansion on an N-dimensional simplex is also discussed. This new expansion is applied to find new cubature formulas for 2-dimensional simplex.

Bernoulli polynomials expansion simplex 

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References

  1. [1]
    F. Costabile, Expansions of real functions in Bernoulli polynomials and applications, Conf. Sem. Univ. Bari 273 (1999).Google Scholar
  2. [2]
    F. Costabile and F. Dell'Accio, Expansion over a rectangle of real functions in Bernoulli polynomials and applications, BIT 41(3) (2001) 451–464.Google Scholar
  3. [3]
    F. Costabile and F. Dell'Accio, On the approximation of C M functions by means of boundary values, Int. J. Appl. Math. 3(1) (2000) 47–61.Google Scholar
  4. [4]
    F. Costabile, M.I. Gualtieri and S. Serra, An iterative method for the computation of the solutions of nonlinear equations, Calcolo 36 (1999) 17–34.Google Scholar
  5. [5]
    H. Engels, Numerical Quadrature and Cubature (Academic Press, 1980).Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • F. Costabile
    • 1
  • F. Dell'Accio
    • 1
  1. 1.Università Degli Studi Della CalabriaItaly

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