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Interpolation and integration based on averaged values. (English) Zbl 1116.41003
Figiel, Tadeuz (ed.) et al., Approximation and probability. Papers of the conference held on the occasion of the 70th anniversary of Prof. Zbigniew Ciesielski, B»©dlewo, Poland, September 20–24, 2004. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 72, 25-47 (2006).
Summary: 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.
For the entire collection see [Zbl 1091.47002].

MSC:
41A05 Interpolation in approximation theory
65D32 Numerical quadrature and cubature formulas
65D25 Numerical differentiation
65D30 Numerical integration
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