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 eective 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.