Automatic Error bounds for Simple Zeros of Analytic Functions The Cauchy-Ostrowski theorem on convergence of Newton iterates for an analytic function in one variable is extended to include computational errors using complex interval arithmetic. Several numerical examples are given for polynomials with real and complex roots and one example for the Bessel function of the first kind. CACM February, 1973 Rokne, J. real intervals, complex intervals, real interval arithmetic, complex interval arithmetic, Newton's method, Cauchy-Ostrowski theorem, zeros of polynomials, zeros of Bessel functions 5.11 5.12 5.15 CA730204 JB January 24, 1978 2:51 PM 1524 4 2544 1931 4 2544 2214 4 2544 2544 4 2544 2544 4 2544 2544 4 2544 1524 5 2544 311 5 2544 2214 5 2544 2544 5 2544 2544 5 2544 2544 5 2544