Rational Approximation

The approximation of functions by rational expressions is important in different disciplines of analysis. First one thinks of the representation of special functions by rational approximations for the use in computers, but the applications go far beyond this point. First, rational approximations arise quite naturally in the numerical solution of ordinary and parabolic differential equations and in the study of other numerical methods. Furthermore, the Stieltjes and the Hamburger moment problem can be well understood via methods from rational approximation. The latter shows that nonlinear approximation theory may be helpful even for problems which originally are convex problems and not nonlinear in a strict sense.