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Successive Adaptive Linear Neural Modeling for Equidistant Real Roots Finding

Abstract:

The main objective of this work has been to implement a model to find equidistant real roots using a Successive Adaptive Linear Neural Modeling which uses two approaches: A Self Organized Map (SOM) and an Adaptative Linear Neuron (Adaline). A SOM model has been used with a new neighborhood function Λ, and a physical distance β with which the task is divided in sub-processes reducing the complexity of the task because the SOM model can delimited the areas where a single root exist. Then, through a successive approach, it is applied an Feed-forward neural model with a learning process base on Adaline neuron with pocket in each pair of regions for finding the real root values with a reduced precision. Finally, several experiments were done consider CPU time, relative error, distance between the roots and polynomial degrees. The results show that the time complexity grows in a linear or logarithmic way. Also, the error does not increase in a higher rate than the degree of polynomial or the root distance.