Conditions for Convergence to a Root Using Iteration Formulae
We can find a root for a functionby equatingto zero and rearranging the equation to givefor some functionOn puttingwe obtain an iteration sequence which will under some circumstance converge to the desired root.
The condition for convergence to a rootis thatand that the starting point for the sequence,be sufficiently close toIfthe sequence iterates to infinity.
Given a function f(x), many rearrangements may be possible. If f(x) has several roots, a sequence may iterate to some fixed point and some other rearrangement is found the sequence may iterate to some other fixed point.