Asymptotically optimal error bounds for quadrature rules of given degree

Error bounds for interpolatory quadrature rules on the unit circle

For the construction of an interpolatory integration rule on the unit circle T with n nodes by means of the Laurent polynomials as basis functions for the approximation, we have at our disposal two nonnegative integers pn and qn, pn + qn = n − 1, which determine the subspace of basis functions. The quadrature rule will integrate correctly any function from this subspace. In this paper upper bou...

A unified generalization of some quadrature rules and error bounds

WENJUN LIU, YONG JIANG, AND ADNAN TUNA Abstract. By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson’s rules, but also give some new error bounds for other quadrature rules as special cases. Especially, two sharp error inequalities are derived when n is ...

Inequalities between the Quadrature Operators and Error Bounds of Quadrature Rules

The order structure of the set of six operators connected with quadrature rules is established in the class of 3–convex functions. Convex combinations of these operators are studied and their error bounds for four times differentiable functions are given. In some cases they are obtained for less regular functions as in the classical results. Quadrature Rules, Inequalities and Error Bounds Szymo...

Quadrature Rules for Fuzzy Integrals

Error Bounds for Gauss-kronrod Quadrature Formulae

The Gauss-Kronrod quadrature formula Qi//+X is used for a practical estimate of the error R^j of an approximate integration using the Gaussian quadrature formula Q% . Studying an often-used theoretical quality measure, for ߣ* , we prove best presently known bounds for the error constants cs(RTMx)= sup \RlK+x[f]\ ll/(l»lloo<l in the case s = "Sn + 2 + tc , k = L^J LfJ • A comparison with the Ga...