Remarks on the Jackson and Whitney Constants
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 phrasesBest approximation Degree of approximation Jackson theorem Whitney constant
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