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Estimation of a Regularisation Parameter for a Robin Inverse Problem

Part of: Integral equations, integral transforms Numerical linear algebra

Published online by Cambridge University Press:  02 May 2017

Xi-Ming Fang ,
Fu-Rong Lin  and
Chao Wang
Xi-Ming Fang
Affiliation:
Department of Mathematics, Shantou University, Shantou Guangdong 515063, China School of Mathematics and Statistic, Zhaoqing University, Zhaoqing Guangdong 526061, China
Fu-Rong Lin
Affiliation:
Department of Mathematics, Shantou University, Shantou Guangdong 515063, China
Chao Wang*
Affiliation:
Department of Mathematics, Shantou University, Shantou Guangdong 515063, China
*
*Corresponding author. Email address:chaowang.hk@gmail.com (C. Wang)
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Abstract

We consider the nonlinear and ill-posed inverse problem where the Robin coefficient in the Laplace equation is to be estimated using the measured data from the accessible part of the boundary. Two regularisation methods are considered — viz. L2 and H1 regularisation. The regularised problem is transformed to a nonlinear least squares problem; and a suitable regularisation parameter is chosen via the normalised cumulative periodogram (NCP) curve of the residual vector under the assumption of white noise, where information on the noise level is not required. Numerical results show that the proposed method is efficient and competitive.

Keywords

Robin inverse problemL2 regularisationH2 regularisationnormalised cumulative periodogram (NCP) method

MSC classification

Secondary: 65F22: Ill-posedness, regularization 65R32: Inverse problems
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 325 - 342
Copyright
Copyright © Global-Science Press 2017 

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