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Volume 5, Issue 4
An Inverse Diffraction Problem: Shape Reconstruction

Yanfeng Kong, Zhenping Li & Xiangtuan Xiong

DOI: 10.4208/eajam.310315.250915a

East Asian J. Appl. Math., 5 (2015), pp. 342-360.

Published online: 2018-02

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  • Abstract

An inverse diffraction problem is considered. Both classical Tikhonov regularisation and a slow-evolution-from-the-continuation-boundary (SECB) method are used to solve the ill-posed problem. Regularisation error estimates for the two methods are compared, and the SECB method is seen to be an improvement on the classical Tikhonov method. Two numerical examples demonstrate their feasibility and efficiency.

  • Keywords

Inverse diffraction problem, ill-posed problems, Tikhonov regularisation, stability estimate, error estimate, SECB.

  • AMS Subject Headings

65J20, 65R35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-342, author = {Yanfeng Kong, Zhenping Li and Xiangtuan Xiong}, title = {An Inverse Diffraction Problem: Shape Reconstruction}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {4}, pages = {342--360}, abstract = {

An inverse diffraction problem is considered. Both classical Tikhonov regularisation and a slow-evolution-from-the-continuation-boundary (SECB) method are used to solve the ill-posed problem. Regularisation error estimates for the two methods are compared, and the SECB method is seen to be an improvement on the classical Tikhonov method. Two numerical examples demonstrate their feasibility and efficiency.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310315.250915a}, url = {http://global-sci.org/intro/article_detail/eajam/10918.html} }
TY - JOUR T1 - An Inverse Diffraction Problem: Shape Reconstruction AU - Yanfeng Kong, Zhenping Li & Xiangtuan Xiong JO - East Asian Journal on Applied Mathematics VL - 4 SP - 342 EP - 360 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.310315.250915a UR - https://global-sci.org/intro/article_detail/eajam/10918.html KW - Inverse diffraction problem, ill-posed problems, Tikhonov regularisation, stability estimate, error estimate, SECB. AB -

An inverse diffraction problem is considered. Both classical Tikhonov regularisation and a slow-evolution-from-the-continuation-boundary (SECB) method are used to solve the ill-posed problem. Regularisation error estimates for the two methods are compared, and the SECB method is seen to be an improvement on the classical Tikhonov method. Two numerical examples demonstrate their feasibility and efficiency.

Yanfeng Kong, Zhenping Li and Xiangtuan Xiong. (2018). An Inverse Diffraction Problem: Shape Reconstruction. East Asian Journal on Applied Mathematics. 5 (4). 342-360. doi:10.4208/eajam.310315.250915a
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