Volume 7, Issue 2
Estimation of a Regularisation Parameter for a Robin Inverse Problem

East Asian J. Appl. Math., 7 (2017), pp. 325-342.

Published online: 2018-02

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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. $L_2$ and $H^1$ 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 problem, $L_2$ regularisation, $H^1$ regularisation, normalised cumulative periodogram (NCP) method.

65F22, 65R32

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@Article{EAJAM-7-325, author = {}, title = {Estimation of a Regularisation Parameter for a Robin Inverse Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {325--342}, 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. $L_2$ and $H^1$ 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150216.260117a}, url = {http://global-sci.org/intro/article_detail/eajam/10752.html} }
TY - JOUR T1 - Estimation of a Regularisation Parameter for a Robin Inverse Problem JO - East Asian Journal on Applied Mathematics VL - 2 SP - 325 EP - 342 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.150216.260117a UR - https://global-sci.org/intro/article_detail/eajam/10752.html KW - Robin inverse problem, $L_2$ regularisation, $H^1$ regularisation, normalised cumulative periodogram (NCP) method. AB -

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. $L_2$ and $H^1$ 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.

Xi-Ming Fang, Fu-Rong Lin & Chao Wang. (2020). Estimation of a Regularisation Parameter for a Robin Inverse Problem. East Asian Journal on Applied Mathematics. 7 (2). 325-342. doi:10.4208/eajam.150216.260117a
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