数值微分的小波最小二乘方法

The least square based on wavelets for numerical differentiation

给出了利用小波求解数值微分的方法。将微分问题转化为等价的第一类Fredholm积分方程,然后选取小波基,使用最小二乘求解该积分方程。我们给出的分析框架容许使用具紧支集的小波,利用正则化保证了计算的稳定性。数值计算实例表明,本方法稳定,运算速度快,计算精度高。

In this paper, the algorithm for numerical differentiation based on wavelets is proposed. We trans- form the differential problems into the Fredholm integral equation of first kind. By selecting the wavelets ba- ses, we use the least square method to solve this supported wavelets in our analysis framework, it perimental results show that our methods are not integral equation. Due to allowance for the use of compact is easily regularized and reduces the computation. The ex- only stable, but also fast and accurate.