ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 46, 65 Fedotov I., Dragomir S. S., University of Transkei, South Africa Another Approach to Quadrature Methods Usually the quadrature error of a quadrature rule is estimated using the high order derivatives of the integrand. In this talk we present new approach to quadrature methods where any formula of numerical integration is generated by discontinouos function whose jumps are quadrature weights. The quadrature error is estimated for continuous and Lipschitz-continuous functions with the constant which can not be replaced by a smaller one. By means of generating function and inequalities of Grüss type we obtain new necessary and sufficient conditions for convergence of any quadrature rule.