Rational approximation of decay-type functions

Numerically given functions with exponential asymptotic behavior are approximated by rational expressions. The numerators are obtained from the nodes of the functions, and the denominators are powers of polynomials, whose coefficients are obtained by expansion in orthogonal polynomials. Different weights are discussed for uniform absolute or relative errors.An iterative procedure is further described to improve the least-squares approximation to one of Chebyshev-type best fit.The research reported in this paper was sponsored in part by the King Gustaf VI Adolf's 70-Years Fund for Swedish Culture, Knut and Alice Wallenberg's Foundation, The Swedish Natural Science Research Council, The Swedish Technical Research Council, and in part by the Aeronautical Research Laboratory, OAR, through the European Office, Aerospace Research, United States Air Force.Part of the work on this paper was carried out while the author was at the Physics Department, University of Florida, Gainesville, Florida, U.S.A.