Parameter identification to an approximated function of the Weierstrass approximation formula

In Weierstrass approximation theorem, a continuous function can be approximated by an algebraic polynomial. In this paper, we use the stochastic gradient identification algorithm and the recursive least squares algorithm to estimate the parameters of the algebraic polynomial. In order to improve the convergence rate and the computational effort, two modified stochastic gradient algorithms are given. The proposed approaches are illustrated by a simulation example.