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Remarks on the Jackson and Whitney Constants

  • Borislav Bojanov
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

The paper is devoted to the constants in the Jackson theorem about approximation of continuous functions by polynomials on [a, b] and the Whitney type estimation of the interpolation error. The Jackson theorem is derived here on the basis of the Tchebycheff alternation theorem. This approach leads to an algorithm for computation of the exact Jackson constant. In the second part we give a new representation of the remainder in the Lagrange interpolation formula and then use it to get estimates of Whitney type for certain classical approximation schemes.

Key words and phrases

Best approximation Degree of approximation Jackson theorem Whitney constant 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Borislav Bojanov
    • 1
  1. 1.Department of MathematicsUniversity of SofiaSofiaBulgaria

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