Function Approximation is a major need in many areas such as Applied Mathematics, Computer Science, Engineering problems and so on. This paper proposed a solution for performing function approximation by using novel functional Chebyshev Neural Network with Backpropagation Algorithm. The advantage of Chebyshev Neural Network is very efficient for computation because of less complexity in modelling of the structure and produces the fast convergence rate and it is easy to implement circuit implementation compared to the standard Multilayer feed forward neural network. The proposed network consists of single input and a single output. The hidden layer is designed as taking the input of numerically transformable Chebyshev polynomial expansion of input. Backpropagation algorithm with Chebyshev Neural Network shows good behaviour in Nonlinear Function Approximation compared to multilayer feed forward neural network. The performance metric used in this paper to compare the realization capability of two networks for training and testing phase is Mean Square Error.

Function Approximation, Chebyshev Neural Network, Multilayer Perceptron, Backpropagation Algorithm

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