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# Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation

@inproceedings{Qin2008ModifiedTR, title={Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation}, author={H. H. Qin and T. Wei and Ran Shi}, year={2008} }

- Published 2008

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a modified Tikhonov regularization algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method.