2544	 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. real intervals complex intervals real interval arithmetic complex interval arithmetic Newton s method Cauchy-Ostrowski theorem zeros of polynomials zeros of Bessel functions
