Interpolation and integration based on averaged values
Volume 72 / 2006
Banach Center Publications 72 (2006), 25-47
MSC: 41A05, 65D32.
DOI: 10.4064/bc72-0-2
Abstract
We discuss recent results on constructing approximating schemes based on averaged values of the approximated function $f$ over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of $f$ over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.
