Euler-Maclaurin and Gregory interpolants (Q907055)

Special types of polynomial interpolants to suitably differentiable approximands are discussed in this paper. Among other things, so-called Gregory interpolants -- whose associated approximation operator is exchangable with integration and that make use of divided differences -- are defined and used in the article. Moreover, Euler-Maclaurin interpolants are given for \(n+1\) equally spaced points that provide approximation operators exchangable with integration too. Here, \(n\) is the degree of the trigonometric polynomial part in the Euler-Maclaurin interpolant. Numerical examples are provided for both types of interpolants.