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An Inverse Diffraction Problem: Shape Reconstruction

Part of: Numerical analysis in abstract spaces

Published online by Cambridge University Press:  10 November 2015

Yanfeng Kong ,
Zhenping Li  and
Xiangtuan Xiong
Yanfeng Kong
Affiliation:
Department of Mathematics, Northwest Normal University, Gansu, China
Zhenping Li
Affiliation:
Department of Mathematics, Luoyang Institute of Science and Technology, Henan, China
Xiangtuan Xiong*
Affiliation:
Department of Mathematics, Northwest Normal University, Gansu, China
*
*Corresponding author. Email address:xiongxt@gmail.com (X. Xiong)
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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 problemill-posed problemsTikhonov regularisationstability estimateerror estimateSECB

MSC classification

Secondary: 65J20: Improperly posed problems; regularization
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 4 , November 2015 , pp. 342 - 360
Copyright
Copyright © Global-Science Press 2015 

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