Sobre una introducción a la teoría de aproximación en espacios normados y de Hilbert

Abstract

The main objective of this paper is to present an introduction to the fundamentals of the approximation theory focused on normed and Hilbert spaces. In Chapter 1, previous concepts which point to the main content are introduced. Chapter 2 introduces the concept of best approximation, additionally, its existence and uniqueness is discussed. Strictly convex normed space is defined, and how the uniqueness of the best approximation is obtained. Depending on the selection of the norm, there are different types of approximations; in Chapter 3 Uniform approximation in C[a,b] and continuous with approximation by Chebyshev polynomials are introduced in Chapter 4. Chapter 5 introduces approximation to Hilbert spaces. The paper concludes with a brief discussion of cubic splines in Chapter 6.