Application of Functional Networks to Solving Functional Equations

In this paper, nine series functional network models for the computation of an approximate real root of a given functional equation are designed. And the computation models for solving some important equations with series functional network and the uniqueness of representation problem are proposed. Some of the neurons in the proposed networks use the given function as their computation units. These computation structures are used for the approximation of unknown or known function by training data sets. We describe the corresponding estimation methods, which are based on minimizing the sum of square errors between the expected and the actual outputs. An illustrative example is also given to clarify concepts and methods. Here we extend that method towards a wide range of functional equations, which can be computation modeled in similar ways to functional equations.