A complex coefficient rational approximation of √1 + cursive chi

Rational approximations of √1 + cursive chi are useful for one-way wave propagation modeling, where a square root operator must be approximated. The standard Padé approximants incorrectly propagate the evanescent modes corresponding to cursive chi <-1. A modification of the Padé approximation is introduced in this paper. Our new approximants have positive real imaginary parts for cursive chi <-1, which give the evanescent modes the desired damping. Mathematical properties of the new approximation are proved in this paper. An efficient numerical method for computing the prime fraction expansion of the new rational approximation is developed. © 1998 IMACS/Elsevier Science B.V.