On the problem of mutual deviation of certain quadrature sums of interpolation type

V.L. Velikin (Oles Honchar Dnipropetrovsk National University)

Abstract


We obtained efficient computational formulae for quadrature sums that are optimal with respect to coefficients for arbitrary distribution of knots for certain classes of differentiable functions. Based on this, we found exact values of mutual deviation of interpolatory type quadrature sums.

Keywords


quadrature sums; spline; interpolation

References



Velikin V.L. "Exact values of approximation by Hermitian splines on the classes of differentible functions", Izv. AN sssr, Ser. matem., 1971; 35(1): pp. 93-124.

Velikin V.L., Korneichuk N.P. "Exact values of approximation by spline-functions on classes of differentiable functions", Matem. zametki, 1971; 9(5): pp. 483-494.

Velikin V.L. "Hermitian splines and quadrature formulas for certain classes of differentiable functions, related to them", Izv. VUZov. Matem., 1976; 168(5): pp. 15-28.

Alberg J., Nilson E., Walsh J., Spline theory and its applications, 1972.

Nikolsky S.M. Quadrature formulae, 1974.

Velikin V.L. "Exact values and bounds of interpolational spreads of certain subspaces of Hermitian splines", Res. Math., 2009; 17: pp. 42-47.




DOI: https://doi.org/10.15421/241212

  

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Copyright (c) 2012 V.L. Velikin

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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