Abstract: Smoothing functions play an important role in Support Vector Machines（SVM），and to find out a good smoothing function is the key to research SVM.The paper derives and proves the performance of a 6th-order smoothing function using the differentiation method，and analyzes its approaching performance using dichotomy.The results show that the approximation accuracy of this 6th-order smoothing functions is better than that of the previously used smoothing functions.So it also provides a new smoothing function for further studying of SVM.

摘要： 光滑函数在支持向量机中起着重要的作用，因此寻找新的光滑函数是研究支持向量机的关键。用求导方法分析了光滑函数的光滑性能，推导并证明了一个六阶光滑函数；同时还用二分法对其逼近性能进行了分析，结果表明：该光滑函数具有比一至五阶光滑函数更高/好的逼近性能，这就为进一步研究支持向量机提供了一个新的光滑函数。