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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-2,
author = {Borislav Bojanov},
title = {Interpolation and integration based on averaged values},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {25-47},
zbl = {1116.41003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-2}
}
Borislav Bojanov. Interpolation and integration based on averaged values. Banach Center Publications, Tome 72 (2006) pp. 25-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-2/