A globally convergent interval method for computing and bounding multiple roots of a once continuously differentiable function

Abstract

This paper showed how Newton’s method can be extended to the several interval Newton methods for locating and bounding multiple and simple roots of a once continuously differentiable function in a given interval. Most of the discussion focused on the theoretical aspect and it had been supported by some numerical evidence. This paper proved that the proposed methods never fail to converge.This paper showed how Newton’s method can be extended to the several interval Newton methods for locating and bounding multiple and simple roots of a once continuously differentiable function in a given interval. Most of the discussion focused on the theoretical aspect and it had been supported by some numerical evidence. This paper proved that the proposed methods never fail to converge.