Nonlinear Approximation Theory

The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approximation is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly t...