Again, the idea is to reduce the number of derivative computations without hurting the convergence of the method.
Modified Newton uses formula () with
If after, say, iterations the speed of convergence
decreases, we need to update the derivative; set
Modified Newton is a method extensively used in scientific and engineering computations.
To obtain the order of convergence, we do the following calculations:
This means that and we say that the Modified Newton method converges linearly. Of course, for convergence we need .