# Alternance Theorems and Chebyshev Splines Approximation

@article{Crouzeix2018AlternanceTA, title={Alternance Theorems and Chebyshev Splines Approximation}, author={Jean-Pierre Crouzeix and Nadezda Sukhorukova and Julien Ugon}, journal={arXiv: Numerical Analysis}, year={2018} }

One of the purposes in this paper is to provide a better understanding of the alternance property which occurs in Chebyshev polynomial approximation and piecewise polynomial approximation problems. In the first part of this paper, we propose an original approach to obtain new proofs of the well known necessary and sufficient optimality conditions. There are two main advantages of this approach. First of all, the proofs are much simpler and easier to understand than the existing proofs. Second…

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