Equioscillation theorem

The equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attributed to Chebyshev.


Let be a continuous function from to . Among all the polynomials of degree , the polynomial minimizes the uniform norm of the difference if and only if there are points such that where .


Several minimax approximation algorithms are available, the most common being the Remez algorithm.


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.