GLOBAL ITERATIVE SOLUTION OF DIELECTRIC-SPECTROSCOPY EQUATIONS

This paper presents a global method to solve the permittivity equations for open-and short-circuited coaxial lines of general length for broad-band measurements by iterating the recurrence schemes Zn+1=c cot Zz, and Zn-1=c tan Zn respectively, and their inverses. The global iteration theory of Fatou and Julia, coupled with linear extrapolation and interpolation and Steffensen’s acceleration procedure, supplies starting values and guarantees convergence even near double roots. When ≥ 0 for open, and É ≤ 0 for short circuit terminations Newton’s method, with appropriate starting values, converges to the desired roots. Thus a combination of the three iterative schemes results in an almost global method of solution. Numerical results are quoted. © 1990 IEEE