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/sub n/+1=c cot z/sub z/ and z/sub n/+1=c tan z/sub 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/sub Z/>or=0 for open, and R/sub Z/>