A Comparison of Different Neural Methods for Solving Iterative Roots

Finding iterative roots is the inverse problem of iteration.Iteration itself plays a major role in numerous theoriesand applications. So far it is hardly realized how manyproblems can be related to its counterpart. This may bedue to the difficulty of the mathematics involved: Thereare no standard methods available for computing thesefractional iterations.Previously we have shown how neural networks can beutilized to perform calculations of iterative roots by addinga weight coupling mechanism to backpropagationlearning. Here we show that an easier implementation ofthis functionality can be achieved by a simple weightcopy function. Introducing second order methods likequasi Newton learning on the other hand can significantlyreduce training times and improve the reliability of themethod. It also overcomes some limitations in the complexityof the problems the method can be applied to