支持向量回归机多项式光滑函数的逼近精度

The approximation accuracies of polynomial smoothing functions for support vector regression

为了解决支持向量回归机多项式光滑函数的逼近精度问题,根据该类光滑函数的复杂性,提出五步求的基本思路: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,接着证明这个逼近函数是一个对称函数,然后分别求出逼近函数在[0,ε]和(ε,+∞)上的最大值,最后对这2个最大值进行比较,得出光滑函数的逼近精度.通过实例计算,结果证明了该方法的有效性和正确性,解决了无穷多个多项式光滑函数的逼近精度问题,为光滑支持向量回归机提供了基本的理论支持.

In order to solve the problem of polynomial smoothing function＇ s approximation accuracies for support vector regression, the researcher proposes to solve the problem utilizing a five step approach, according to the com- plexity of smooth functions. The first step, examines the problem of the approximation accuracy in the polynomial smoothing function represented by solving the maximum value of an approximation function; second, the function was verified to be a symmetric function; third, the maximum values of the approximation function were derived re- spectively at the intervals [0,ε] and （ε, ＋ ∞） ; fourth, the two maximum values were compared, and finally the approximation accuracy was obtained. Through the calculation with examples, the correctness and effectiveness of the method was validated, and the approximation accuracy problem of the infinite polynomial smoothing functions was systematically solved in this paper, which offers basic theoretical support for smooth support vector regression.