Error bounds for interpolatory quadrature rules on the unit circle

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...

Positive trigonometric quadrature formulas and quadrature on the unit circle

We give several descriptions of positive quadrature formulas which are exact for trigonometric-, respectively, Laurent polynomials of degree less or equal to n − 1 − m, 0 ≤ m ≤ n − 1. A complete and simple description is obtained with the help of orthogonal polynomials on the unit circle. In particular it is shown that the nodes polynomial can be generated by a simple recurrence relation. As a ...

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