PP-TSVD方法及在数值微分问题中的应用

PP-TSVD approach and its application in numerical differentiation

数值微分问题是不适定的,为了得到近似已知函数稳定的近似导数,并且能够很好地反映导数的间断情况,本文讨论了PP-TSVD方法,其正则解可以在没有任何先验信息的情况下反映解的间断性,将这种方法应用于数值微分问题,数值实验说明这种方法对反映导数的间断情况十分有效.

Numerical differentiation is always ill-posed. In order to obtain stable approximate derivative to the given functions, and to well display the discontinuity of the derivative, this paper discusses the PP-TSVD approach whose regularization solution can display its discontinuity without specifying any prior information. This paper then applies this method in numerical differentiation, and the numerical experiments has illustrated that this method is very effective to display the discontinuity of derivative.