Approximation accuracies of a class of polynomial smoothing functions

Abstract

In 2007 Xiong et al.proposed a class of polynomial smoothing functions whose approximation accuracy is a problem that has not been solved.This paper applied dichotomy algorithm to solve the problem.To overcome the shortcoming that the root might be missed by dichotomy algorithm the problem of approximation accuracy for smoothing function was firstly expressed by the problem of solving the maximum value of approximation function and the approximation function was divided into 4 segments and the maximum value of the each segment was sought respectively then the maximum value of approximation function was obtained in the whole x-axis.Taking 1st-order and 2nd-order smooth polynomial functions as examples whose approximation accuracies were solved by the dichotomy algorithm.The results show that the dichotomy algorithm is a effective way to solve the approximation accuracy for this class of smoothing functions of support vector machine.