Journal of Online Mathematics and Its Applications

Volume 6. December 2006. Article ID 1316

The Chebyshev Equioscillation Theorem

Robert Mayans

Contents

1. Introduction
2. The Weierstrass approximation theorem
3. The polynomial of best approximation
4. Alternating sets
5. Lower bounds on the minimax error
6. Sectioned alternating sets
7. Improving the approximation
8. Proof of the theorem
9. Finding the minimizing polynomial
10. Notes and resources