Chebyshev's approximation

Chebyshev's approximation is a method used to find the best possible polynomial that closely matches a function across a specific interval. Unlike simple fitting methods, it minimizes the maximum error between the original function and the polynomial, ensuring the largest difference at any point is as small as possible. This creates a uniform approximation, reducing even the worst deviations and resulting in a more accurate and reliable representation of the original function across the entire interval. It's widely used in numerical analysis to efficiently approximate complex functions with simpler polynomial expressions.