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Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey. (English) Zbl 0990.41003
In this short survey, the authors present some recent procedures for constructing optimal interpolation processes, i.e., the processes with Lebesgue constants having logarithmic behavior, in the uniform metric on $\left[-1,1\right]$. The paper contains several known results and the following new result: the authors prove that, if we add a suitable number of knots near the endpoints of $\left[-1,1\right]$ to the zeros of the associated Jacobi polynomials, we obtain an interpolation process with optimal Lebesgue constant.
##### MSC:
 41A05 Interpolation (approximations and expansions) 42C05 General theory of orthogonal functions and polynomials 33C45 Orthogonal polynomials and functions of hypergeometric type