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We consider optimal Lagrange interpolation with polynomials of degree at most two on the unit interval [−1, 1]. In a largely unknown paper, Schurer (1974, Stud. Sci. Math. Hung. 9, 77-79) has… (More)

A famous unsolved problem in the theory of polynomial interpolation is that of explicitly determining a set of nodes which is optimal in the sense that it leads to minimal Lebesgue constants. In [11]… (More)

The problem to determine an explicit one-parameter power form representation of the proper Zolotarev polynomials of degree $n$ and with uniform norm $1$ on $[-1,1]$ can be traced back to P. L.… (More)

In the theory of interpolation of continuous functions by algebraic polynomials of degree at most n− 1 ≥ 2, the search for explicit analytic expressions of extremal node systems which lead to the… (More)

- Heinz-Joachim Rack
- Periodica Mathematica Hungarica
- 2014

We consider real univariate polynomials $$P_n$$Pn of degree $$ \le n $$≤n from class $$\begin{aligned} \mathbf {C}_n = \{P_n:|P_n \left( \cos \displaystyle \frac{(n -i)\pi }{n}\right) |\le 1 \;… (More)