Rational approximation of empirical functions

A method is developed for finding the best rational approximationp(x)/q(x) in the least-squares sense of a functionf(x) known at discrete points of an interval. Especially for functions with a steep tangent the method yields far better results than polynomial approximation. The scheme can easily be extended to functions known at all points of an interval.Part of this work was carried out at SAAB, Linköping. The present form was developed at the Department of Numerical Analysis, Lund.