The Chebyshev-polynomials-based unified model neural networks forfunction approximation

摘要

In this paper, we propose the approximate transformable technique,nwhich includes the direct transformation and indirect transformation, tonobtain a Chebyshev-Polynomials-Based (CPB) unified model neural networksnfor feedforward/recurrent neural networks via Chebyshev polynomialsnapproximation. Based on this approximate transformable technique, wenhave derived the relationship between the single-layer neural networksnand multilayer perceptron neural networks. It is shown that the CPBnunified model neural networks can be represented as a functional linknnetworks that are based on Chebyshev polynomials, and those networks usenthe recursive least square method with forgetting factor as learningnalgorithm. It turns out that the CPB unified model neural networks notnonly has the same capability of universal approximator, but also hasnfaster learning speed than conventional feedforward/recurrent neuralnnetworks. Furthermore, we have also derived the condition such that thenunified model generating by Chebyshev polynomials is optimal in thensense of error least square approximation in the single variable ease.nComputer simulations show that the proposed method does have thencapability of universal approximator in some functional approximationnwith considerable reduction in learning time