Interpolation

The process of constructing a function which takes on given data values at given data points is called interpolation. In a certain sense, interpolation is a special case of discrete approximation, but the subject deserves a separate and detailed treatment. The results of the theory of interpolation are a basic part of the constructive theory of functions, and moreover, provide the basis for a wide variety of methods for numerical integration, numerical treatment of differential equations, and the discretization of general operator equations.