磨光法的一个应用

给出了在工程技术中常见的间断周期函数 f(x) .运用对函数进行磨光法得到的具有二阶连续导数 ,作为原来函数 f(x)的最佳逼近元 ,与其它的逼近函数进行比较 ,分析了各自的优缺点 .磨光函数能克服其它逼近函数的缺点 ,同时具有与三次样条函数相同的精度 ,而且计算简单 ,应用广泛

An Application of the Polish Method

For discontinuous periodic function in engineering, a polished function which has continuous derivative of second order can be obtained with the polished method. As an element of best approximation comparing with other approximating function, it gives the advantages and disadvantages of various functions. The polished function does not have the weakness of other approximating function, But there are simple calculation and good precision as the cubic spline function.