On the Convergence of Some Interval-Arithmetic Modifications of Newton’s Method
Götz E. Alefeld · SIAM Journal on Numerical Analysis · 1984
In this paper we consider the meanwhile well-known interval-arithmetic modifications of the Newton's method and of the so-called simplified Newton’s method for solving systems of nonlinear equations. Starting with an interval-vector which contains a zero, we give for the first time sufficient conditions for the convergence of these methods to this solution. If the starting interval-vector contains no solution, then under the very same conditions the methods under consideration will break down after a finite number of steps. The interval-arithmetic evaluation of the first derivative is only involved in these conditions.