Costabile, F. A.; Dell’Accio, F. Expansion over a rectangle of real functions in Bernoulli polynomials and applications. (English) Zbl 0989.65014 BIT 41, No. 3, 451-464 (2001). A new expansion of a sufficiently smooth univariate real function in terms of Bernoulli polynomials has been given by F. Costabile [Conf. Sem. University Bari, N 273 (1999)]. The authors generalise this expansion for the bivariate case. Using this, some useful kernels are obtained which are substantially different from Sard kernel for a wide class of linear functional that includes the truncated error for cubature formulas. Reviewer: H.P.Dikshit (New Delhi) Cited in 26 Documents MSC: 65D15 Algorithms for approximation of functions 65D32 Numerical quadrature and cubature formulas Keywords:Bernoulli polynomial; Taylor expansion; Sard kernel; linear functional; cubature formulas PDFBibTeX XMLCite \textit{F. A. Costabile} and \textit{F. Dell'Accio}, BIT 41, No. 3, 451--464 (2001; Zbl 0989.65014) Full Text: DOI