# 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.

## Statement

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 .

## Algorithms

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

## References

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

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