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 - <p style="text-align: justify;">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.</p>