A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION

doi:10.1016/S0252-9602(15)30058-8

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	A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION
	Yang, Fan 1,2; Fu, Chuli 2; Li, Xiaoxiao 1
刊名	ACTA MATHEMATICA SCIENTIA
	2015-11
卷号	35 期号:6 页码:1339-1348
关键词	Cauchy problem for Laplace equation ill-posed problem a posteriori parameter choice error estimate
ISSN号	0252-9602
DOI	10.1016/S0252-9602(15)30058-8
英文摘要	In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.
资助项目	Natural Science Foundation of Gansu province[1310RJYA021]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000365374100006
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/33946]
专题	理学院
通讯作者	Yang, Fan
作者单位	1.Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China 2.Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
推荐引用方式 GB/T 7714	Yang, Fan,Fu, Chuli,Li, Xiaoxiao. A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION[J]. ACTA MATHEMATICA SCIENTIA,2015,35(6):1339-1348.
APA	Yang, Fan,Fu, Chuli,&Li, Xiaoxiao.(2015).A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION.ACTA MATHEMATICA SCIENTIA,35(6),1339-1348.
MLA	Yang, Fan,et al."A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION".ACTA MATHEMATICA SCIENTIA 35.6(2015):1339-1348.