In this paper we study the remainder of interpolatory quadrature formulae. For this purpose
we develop a simple but quite general comparison technique for linear functionals. Applied …

In this paper we derive cubature error bounds for the product rule generated by two Gauss-
Legendre quadrature rules. An analogue to the fundamental theorem of algebra, for …

We study the error of rational quadrature rules when functions which are analytic on a
neighborhood of the set of integration are considered. A computable upper bound of the …

1. Introduction. Clenshaw and Curtis [1] have proposed a quadrature scheme based on the"
practical" abscissas xi= cos (iir/n), i= O (1) n and they have also discussed the estimation of …

ERROR BOUNDS BASED ON APPROXIMATION THEORY IR(f] I = IR[I - u]1 $ IIRII III - ull Page
1 ERROR BOUNDS BASED ON APPROXIMATION THEORY H. Brass Institut f'tir Angewandte …

Interpolatory quadrature rules exactly integrating rational functions on the unit circle are
considered. The poles are prescribed under the only restriction of not lying on the unit circle …

Approximate rules for evaluating linear functionals are often obtained by requiring that the
rule shall give exact value for a certain linear class of functions. The parameters of the rule …

This note is continuation of the recent pper with the sme title [3]. Inorder to mke it
independently readable we re-state briefly the connection between monosplines nd …

In certain spaces of analytic functions the error term of a quadrature formula is a bounded
linear functional. We give a survey of the methods used in order to compute explicitly, or in …

The starting point of this paper is a theorem, based on the theory of functions of a complex
variable, which essentially gives a representation of the remainder in a quadrature rule as a …