A COMPLEX COEFFICIENT RATIONAL APPROXIMATION OF ROOT-1+X

Rational approximations of root 1 + x are useful for one-way wave prop agation modeling, where a square root operator must be approximated. T he standard Pade approximants incorrectly propagate the evanescent mod es corresponding to x < -1. A modification of the Pade approximation i s introduced in this paper. Our new approximants have positive real im aginary parts for x < -1, which give the evanescent modes the desired damping. Mathematical properties of the new approximation are proved i n this paper. An efficient numerical method for computing the prime fr action expansion of the new rational approximation is developed. (C) 1 998 IMACS/Elsevier Science B.V.