Approximation by Chebyshev Polynomials

Approximation by Chebyshev polynomials involves using these special mathematical functions to closely match other, more complex functions within a certain range. Chebyshev polynomials are designed to minimize the maximum error between the polynomial approximation and the original function, leading to highly accurate representations with fewer terms. This method effectively reduces the worst-case deviation, providing a efficient and stable way to approximate functions in numerical analysis, engineering, and scientific computations. It’s a powerful technique to simplify difficult functions while maintaining high accuracy, especially useful when performance and precision are critical.