A Globally Convergent Interval Newtons Method for Computing and Bounding Real Roots of a Function with One Variable
Yosza Dasril, Ismail Mohd · International Journal of Mathematics in Operational Research · 2020
It is known that Newton's method is locally convergent, involves errors in numerical computations, and requires an initial guess point for calculating. This initial guess point should be closed enough to the root or zeros otherwise this method fails to converge to the desired root. The method of interval mathematics should overcome these issues and be used to make Newton's method as globally convergent. This paper shows how to use interval mathematics for computing and bounding the simple and multiple roots of multimodal functions. It shows how to solve the problem when zero is in the given interval. The numerical computations for the two examples show the ability of newly proposed methods and satisfactory computational behaviour and convince us that Newton's method is able to solve nonlinear problems statement.