Quadrature formulae of non-standard type

Abstract

We discuss quadrature formulae of highest algebraic degree of precision for integration of functions of one or many variables which are based on non-standard data, i.e., in which the information used is different from the standard sampling of function values. Among the examples given in this survey is a quadrature formula for integration over the disk, based on linear integrals on n chords, which integrates exactly all bivariate algebraic polynomials of degree 2n − 1.

Keywords

• gaussian formula
• numerical integration
• multivariate functions