## On optimization of formulae for approximate integration on various classes of univariate and multivariate functions

- Nov. 15, 2007
- 3:30 p.m.
- LeConte 312

## Abstract

In this talk a survey of results on optimization of quadrature and cubature formulae on various classes of univariate and multivariate functions, obtained by author throughout the years will be given. New results in this direction will also be presented. In particular, the problem of optimizing interval quadrature formulae on various classes of functions is considered, and the optimality of "averaged" rectangles formulae on classes of periodic functions which can be represented as a convolution with a kernel that does not increase the oscillation with functions from an arbitrary shift invariant set is proved.