Compact Integration Rules as a quadrature method with some applications

Weighted quadrature rules with binomial nodes

In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...

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 ...

Quadrature Rules for Fuzzy Integrals

Quadrature rules with multiple nodes

In this paper a brief historical survey of the development of quadrature rules with multiple nodes and the maximal algebraic degree of exactness is given. The natural generalization of such rules are quadrature rules with multiple nodes and the maximal degree of exactness in some functional spaces that are different from the space of algebraic polynomial. For that purpose we present a generaliz...

Some Remarks on the Construction of Extended Gaussian Quadrature Rules

We recall some results from a paper by Szego on a class of polynomials which are related to extended Gaussian quadrature rules. We show that a very efficient algorithm, for the computation of the abscissas of the rules in question, was already described in that paper. We also point out that this method extends to rules for integrals with an ultraspherical-type weight function. A bound for the e...