In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

The course title, approximation theory, covers a great deal of mathematical territory. In the present context, the focus is primarily on the approximation of real-valued continuous functions by some …

Approximation theory is the branch of mathematics which studies the process of approximating general functions by simple functions such as polynomials, finite elements or Fourier series.

Approximation Theory The primary aim of a general approximation is to represent non-arithmetic quantities by arithmetic quantities so that the accuracy can be ascertained to a desired degree.

I now again regard approximation theory as exceedingly close to computing, and in this book we shall discuss many practical numerical problems, including interpolation, quadrature, rootfinding, analytic …

Every continuous function on a bounded interval can be approximated to arbitrary accuracy by polynomials. This is the famous Weierstrass approximation theorem, proved by Karl Weierstrass …

If approximation is our goal, interpolation is only one means to that end. In this chapter we investigate alternative approaches that directly optimize the quality of the approximation.

Suppose we are given a sequence (Un) of subsets of X. Degree of approximation considers the behaviour of En(f) := dist(f, Un) as a function of the parameter n as n → ∞.

Nov 14, 2025 · Approximation theory also studies the size and properties of the error introduced by approximation. Approximations are often obtained by power series expansions in which the higher …

This well-written textbook provides an elementary introduction to approximation theory. The authors concentrate on the presentation of main ideas and demonstrate the great influence of classical …