`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
.
`