On some examples and counterexamples of the Runge phenomena and Chebyshev nodes
Résumé
Runge's phenomenon appears in the interpolation process using uniformly placed nodes for some smooth function. An effective solution to this problem is the use of Chebychev roots as interpolation nodes. In this paper, we discuss the efficiency of these nodes and give many illustrated counterexamples of some differentiable and non-differentiable functions to show the limitation of the used Chebychev roots as nodes for Lagrange interpolation.
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Références
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