Asymptotics of polynomial interpolation and the Bernstein constants. (English) Zbl 1468.41005
The author studies new asymptotic bounds for the quantities of the classical Lagrange interpolation error for \(|x|a\), \(a > 0\) when a tends to infinity. Moreover, he gives some explicit constructions for near best approximation polynomials to \(|x|a\), \(a > 0\) in the \(L_\infty\) norm which are based on the Chebyshev interpolation process. Some numerical examples are given.
Reviewer: Antonio López-Carmona (Granada)
MSC:
| 41A05 | Interpolation in approximation theory |
| 41A10 | Approximation by polynomials |
| 65D05 | Numerical interpolation |
References:
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