数值微分问题的两种正则化方法研究

Two regular methods for numerical differential problems

随着工业水平的不断发展和科学技术的不断进步,数值微分问题的正则化逐渐受到研究人员的重视。现如今正则化已经是数学领域的重要研究课题之一,尤其是近些年,相关的研究成果层出不穷。本文从数值微分和正则化的相关理论出发,简要分析了反问题与不适定问题的内涵,并对Fourier截断方法及修改核方法进行了一定程度的研究。

With the development of industrial level of science and technology, regularization of numerical differential problems are paid great attention by researchers. Now the regularization is one of important research topics in mathematics field, especially in recent years, the related research results emerge in an endless stream. This paper starts from the related theories of numerical differentiation and regularization, briefly analyzes the connotation of inverse problems and ill posed problem, and the truncated Fourier method and modified kernel method has been studied to some extent.