A Complex Coe cient Rational Approximation of p 1 + xYa

Rational approximations of p 1 + x are useful for one-way wave propagation modeling, where a square root operator must be approximated. The standard Pad e approximants incorrectly propagate the evanescent modes corresponding to x < ?1. A modiication of the Pad e approximation is introduced in this paper. Our new approximants have positive real imaginary parts for x < ?1, which give the evanescent modes the desired damping. Mathematical properties of the new approximation are proved in this paper. An eecient numerical method for computing the prime fraction expansion of the new rational approximation is developed.