A MODIFIED PRONY ALGORITHM FOR FITTING FUNCTIONS DEFINED BY DIFFERENCE-EQUATIONS

Abstract

This paper reformulates, generalizes, and investigates the stability of the modified Prony algorithm introduced by Osborne [SIAM J. Numer. Anal. 12 (1975), pp. 571–592], with special reference to rational and exponential fitting. The algorithm, originally for exponential functions, is generalized to the least squares fitting of any function which satisfies a linear homogeneous difference equation. Using the difference equation formulation, the problem is expressed as a separable regression, and hence as a nonlinear eigenproblem in terms of the coefficients of the difference equation. The eigenproblem involves finding the null space of a matrix of data differences B, and is solved using a var..