Abstract: This chapter presents the main mathematical results behind Chebyshev tensors and interpolants as function approximators. Polynomial functions are a well-understood family of functions used in various areas of mathematics. One of the main advantages of working with Chebyshev points is that polynomial interpolation on Chebyshev points has the same convergence properties as Chebyshev projections. The Runge function is a dramatic example of an analytic function for which equidistant interpolation yields exponential divergence, while Chebyshev interpolation yields exponential convergence. The family of Chebyshev points is not the only one with an associated potential field that attains minimal energy. The chapter shows that Chebyshev interpolants carry their special approximation properties through to their derivatives. When a polynomial interpolant, even a Chebyshev one, is built to approximate it, a series of oscillations around the discontinuity appear that cannot be resolved regardless of the size of the grid.
Publication Year: 2021
Publication Date: 2021-12-16
Language: en
Type: other
Indexed In: ['crossref']
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot