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Error of truncated Chebyshev series and other near minimax polynomial approximations. (English) Zbl 0623.41004

Authors’ abstract: It is well known that a near minimax polynomial approximation P is obtained by truncating the Chebyshev series of a function f after \(n+1\) terms. It is shown that if \(f\in C^{(n+1)}[- 1,1]\), then \(\| f-p\|\) may be expressed in terms of \(f^{(n+1)}\) in the same manner as the error of minimax approximation. The result is extended to other types of near minimax approximation.
Reviewer: E.Deeba

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
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