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Ukrainian Mathematical Journal

, Volume 64, Issue 8, pp 1151–1167 | Cite as

Approximation of some classes of functions of many variables by harmonic splines

  • V. F. Babenko
  • T. Yu. Leskevich
Article

We determine the exact values of the upper bounds of the errors of approximation by harmonic splines for functions u defined on an n-dimensional parallelepiped Ω and such that ||Δu|| L∞(Ω) ≤ 1 and functions u defined on Ω and such that ||Δu|| L∞(Ω) ≤ 1, 1 ≤ p ≤ ∞. In the first case, the error is estimated in L p (Ω). 1 ≤ p ≤ ∞. In the second case, the error is estimated in L 1(Ω).

Keywords

Green Function Interpolation Polynomial Arbitrary Solution Piecewise Polynomial Function Polyhedral Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • V. F. Babenko
    • 1
    • 2
  • T. Yu. Leskevich
    • 1
  1. 1.Dnepropetrovsk National UniversityDnepropetrovskUkraine
  2. 2.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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