A convergence acceleration procedure for computing slowly converging series

Author

Singh, Surendra ; Singh, Ritu

Author_Institution

Dept. of Electr. Eng., Tulsa Univ., OK, USA

Volume

40

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

168

Lastpage

171

Abstract

The application of shaped θ-algorithm to the partial sums of a slowly converging series is shown to accelerate its convergence. The algorithm is applied to accelerate the convergence of a series representing the free-space periodic Green´s functions involving the zeroth-order Hankel function of the second kind, and its associated Fourier transform. Numerical results indicate that the algorithm converges faster than Shanks´ transform. It is also able to sum the series to machine precision in about 20 terms. A relative error measure is shown as a function of the number of terms of various combinations of source and observation points. The relative savings in computation time is also provided to show the benefit of using the algorithm

Keywords

Green´s function methods; convergence of numerical methods; series (mathematics); Fourier transform; convergence acceleration procedure; free-space periodic Green´s functions; partial sums; relative error measure; shaped &thetas;-algorithm; slowly converging series; zeroth-order Hankel function; Acceleration; Convergence; Fourier transforms; Green´s function methods; Microwave theory and techniques; Phased arrays;

fLanguage

English

Journal_Title

Microwave Theory and Techniques, IEEE Transactions on

Publisher

ieee

ISSN

0018-9480

Type

jour

DOI

10.1109/22.108339

Filename

108339