A complex coefficient rational approximation of 1+x Original Research Article

Rational approximations of View the MathML source 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 x < −1. A modification of the Padé 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 efficient numerical method for computing the prime fraction expansion of the new rational approximation is developed.