A robust implementation of the Caratheodory-Fejer method for rational approximation

摘要

Best rational approximations are notoriously difficult to compute. How ever, the difference between the best rational approximation to a function and its Caratheodory-Fejer (CF) approximation is often so small as to be negligible in prac tice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the Chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software.