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The Divergence of Lagrange Interpolation for |x| at Equidistant Nodes
Authors:Michael Revers
Affiliation:Department of Mathematics, University Salzburg, Hellbrunnerstrasse 34, A-5020, Salzburg, Austriaf1
Abstract:In 1918 S. N. Bernstein published the surprising result that the sequence of Lagrange interpolation polynomials to |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange interpolation polynomials corresponding to |x|α (0<α1) on equidistant nodes in [−1, 1] diverges everywhere in the interval except at zero and the end-points.
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