一类多项式光滑函数的逼近精度

针对一类支持向量机的多项式光滑函数，采用二分法求解它们尚未解决的逼近精度问题。为克服二分法可能会漏根的缺点，首先把多项式光滑函数的逼近精度问题表示为一个求逼近函数的最大值问题，把这个逼近函数分成4 段，分别求出每段的最大值，然后得到逼近函数在整个x轴上的最大值。并以1阶和2阶多项式光滑函数为例，用二分法解决了它们的逼近精度问题。研究表明，二分法是求解这类多项式光滑函数逼近精度的有效方法。

Approximation accuracies of a class of polynomial smoothing functions

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.