General Approach to Function Approximation

Abstract

Applying a predefined set of functionals to a function provides a set of numbers which characterize the function. One can then interpret an approximation very generally as a construction of some function form which reproduces these numbers if the same functionals are used. A large number of existing approximations can be interpreted in this way, and we review some of them. In addition, we construct several new expansion types including three rational approximations.