Systolic algorithm for rational interpolation and Padé approximation

This paper describes a systolic algorithm for rational interpolation based on Thiele's reciprocal differences. This algorithm constructs the continued fraction/Pade approximant of a stream of input data using a linear array of processors. The period of this algorithm is O(n+1) (where n+1 is the number of distinct points at which the function values are available) to produce an M/M Padé approximant ( M = n+1/2, n odd; M= n/2, n even) using n + 1 processors. For illustrative purpose the Connection Machine implementation of this systolic algorithm in CM Fortran is presented with an example