Global iterative solution of dielectric spectroscopy equations

A global method is presented for solving the permittivity equations for open- and short-circuited coaxial lines of general length for broadband measurements by iterating the recurrence schemes z_n+1=c cot z_z and z _n+1=c tan z_n, respectively, and their inverses. The global iteration theory of Fatou and Julia (see J. L. Howland and R. Vaillancourt, Num. Math., vol.46, 323-337, 1985), coupled with linear extrapolation and interpolation and Steffensen's acceleration procedure, supplies starting values and guarantees convergence even near double roots. When R_Z⩾0 for open, and R_Z⩽0 for short circuit terminations Newton's method, with appropriate starting values, converges to the desired roots. A combination of the three iterative schemes results in an almost global method of solution. Numerical results are quoted