Interpolation and integration based on averaged values

Volume 72 / 2006

Borislav Bojanov 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.

Authors

  • Borislav BojanovDepartment of Mathematics
    University of Sofia
    Blvd. James Bourchier 5
    1164 Sofia, Bulgaria
    e-mail

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