Expansion Over a Rectangle of Real Functions in Bernoulli Polynomials and Applications
In this paper we generalize an expansion in Bernoulli polynomials for real functions possessing a sufficient number of derivatives. Starting from this expansion we obtain useful kernels, which are substantially different from Sard's for a wide class of linear functionals that includes the truncation error for cubature formulas.
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- 1.F. Costabile, Expansions of real functions in Bernoulli polynomials and applications, Conf. Sem., University Bari, N. 273, 1999.Google Scholar
- 2.F. Costabile and F. Dell'Accio, Expansion over a simplex of real functions by means of Bernoulli polynomials and applications, submitted.Google Scholar
- 3.F. Costabile, M. I. Gualtieri, and S. Serra, An iterative method for the computation of the solutions of nonlinear equations, Calcolo, 36 (1999), pp. 17-34.Google Scholar
- 4.P. J. Davis, Interpolation and Approximation, Dover, New York, 1975.Google Scholar
- 5.H. Engels, Numerical Quadrature and Cubature, Academic Press, London, 1990.Google Scholar
- 6.C. Jordan, Calculus of Finite Differences, Chelsea, New York, 1965.Google Scholar
- 7.A. Sard, Linear Approximation, Amer. Math. Soc., Math. Surveys, N9, 1963.Google Scholar
- 8.D. D. Stancu, The remainder of certain linear approximation formulas in two variables, J. SIAM Numer. Anal., Ser. B, 1 (1964), pp. 137-163.Google Scholar
- 9.J. F. Steffensen, Interpolation, Chelsea, New York, 1965.Google Scholar