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 .
- Notes on how to prove Chebyshev’s equioscillation theorem at the Wayback Machine (archived July 2, 2011)
- The Chebyshev Equioscillation Theorem by Robert Mayans