Modified Prony Method for Integration of Highly Oscillating Functions

Abstract

In this work we propose a modified Prony interpolation (MPI) technique for the integration of highly oscillating functions appearing in various engineering problems, like electrically large scattering or physical optics problems. We develop a quadrature for the numerical integration over a finite domain [a, b]. In domain [a, b], the integrand function is appropriately interpolated using Prony’s method, taking into account the optimal estimation of the complex exponents existing in the interpolation formula. This optimal selection is chosen by examining the principal value of the involved logarithm, and allows for improved convergence. The convergence and accuracy of the MPI method is demonstrated by comparisons with the alternative Gauss-Kronrod quadrature, which is suitable for integrating highly oscillating functions. Different numerical results are presented. Represented numerical results.