Uniform Approximation

a type of approximation of a function. In uniform approximation, the “distance” on a given set between the given function f(x) and the approximating function P(x) is measured by the least upper bound of the absolute value of their difference. For example, the distance between the continuous function P(x) and the continuous function f(x) on the closed interval [a, b] is

Uniform approximation is also referred to as Chebyshev approximation, in honor of P. L. Chebyshev, who studied it in 1854. (SeeAPPROXIMATION AND INTERPOLATION OF FUNCTIONS.)