矩形区域上Helmholtz方程Cauchy 问题的几种正则化方法

兰州大学机构库 >数学与统计学院

	矩形区域上Helmholtz方程Cauchy 问题的几种正则化方法
Alternative Title	Some regularization methods for the Cauchy problem for theHelmholtz equation in the rectangular region
	李维金
Thesis Advisor	傅初黎
	2009-05-21
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	不适定问题 Helmholtz方程截断正则化方法最小二乘法对偶最小二乘法误差估计
Abstract	本文研究矩形区域上Helmholtz方程Cauchy 问题，这类问题是经典的严重不适定问题。对仅具有非齐次Dirichlet数据的Cauchy问题考虑其最优误差界，并用截断正则化方法、离散正则化方法进行正则化处理，用截断正则化方法对仅具有非齐次Neumann数据的Cauchy问题进行正则化处理。这些正则化方法均得到很强的收敛性估计，恢复解在边界上的稳定性。截断正则化方法的数值例子表明这个方法是可行的。
Other Abstract	In this paper the Cauchy problem for the Helmholtz equation in the rectangular region is considered,it is severely ill-posed problem.We consider the optimal error estimate for the Cauchy problem with only nonhomogeneous Dirichlet data on the boundary, use truncated regularization method, discrete regularization method to solve this problem. Truncated regularization method is used to deal with the Cauchy problem with only nonhomogeneous Neumann data on the boundary. The convergence estimates are obtained for all these regularization methods.Numerical example for truncated regularization method shows that the method works well.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/224997
Collection	数学与统计学院
Recommended Citation GB/T 7714	李维金. 矩形区域上Helmholtz方程Cauchy 问题的几种正则化方法[D]. 兰州. 兰州大学,2009.

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