中文摘要：

光滑支持向量机（SSVM）可以用牛顿法等快速算法求解,典型的光滑函数有sigmoid函数的积分函数、多项式函数、插值函数和样条函数。本文从理论和数值实验两个方面比较研究了这些光滑函数逼近正号函数的精度及SSVM模型的常用求解算法Newton-Armijo法、BFGS-Armijo法和Newton-PCG法的收敛速度。研究表明,光滑函数越逼近正号函数,解的精度越高,而训练时间也明显增加;Newton-Armijo法的收敛速度慢于后两种方法,而Newton-PCG法收敛速度最快。

英文摘要：

Smoothing support vector machine（SSVM）can be solved by Newton algorithm and other fast algorithms.The classical smooth functions include the integral of sigmoid function,polynomial function,interpolation function,splines function and so on.From theoretic and numerical experiment,the paper compares and studies the accuracy of popular smooth functions approximating plus function and the convergence speed of the favorite algorithm for SSVM including Newton-Armijo algorithm,BFGS-Armijo algorithm and Newton-PCG algorithm.It is shown that the more the smooth function approximates plus function,the more accurate the solution is,while the train time is heavily increased.Newton-PCG algorithm is the fastest one,and NewtonArmijo algorithm is the slowest one.