Estimation of a Regularisation Parameter for a Robin Inverse Problem. Issue 2 (2nd May 2017)

• Record Type: Journal Article
• Authors: Fang, Xi-Ming; Lin, Fu-Rong; Wang, Chao
• Is Part Of: East Asian journal on applied mathematics. Volume 7:Issue 2(2017)
• Page Start: 325
• Page End: 342
• Publication Date: 2017-05-02
• Subjects: 65F22, -- 65R32; Robin inverse problem, -- L2 regularisation, -- H2 regularisation, -- normalised cumulative periodogram (NCP) method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.150216.260117a
• Languages: English
• ISSNs: 2079-7362

Abstract

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.