Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4663528 | Acta Mathematica Scientia | 2015 | 10 Pages |
Abstract
In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.
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