Nonlinear Approximation Theory

The exploration of nonlinear approximation problems, initiated by P.L. Chebyshev, reveals a deep connection to uniform approximation theory. Over the years, advancements have led to the development of best uniform approximation techniques using rational functions and polynomials. The distinction between linear and nonlinear approximation emerged in the 1960s, highlighting the need for nonlinear functional analysis and topological methods. This book delves into the application of these methods, including their relevance to linear approximation challenges, such as moment problems and polynomial interpolation.