Jackson’s Theorem

Jackson’s Theorem is a result in approximation theory stating that any continuous function can be closely approximated by a polynomial, with the quality of approximation depending on the function’s smoothness. Specifically, it provides a way to determine how well a polynomial of a certain degree can mimic a given function, ensuring that as you increase the degree, the approximation becomes more accurate. This theorem helps us understand the limits and capabilities of polynomial approximations in modeling complex functions, which is fundamental in numerical analysis and applied mathematics.