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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 1468634, 9 pages
http://dx.doi.org/10.1155/2016/1468634
Research Article

Optimal Stable Approximation for the Cauchy Problem for Laplace Equation

College of Science, China University of Petroleum (East China), Qingdao 266580, China

Received 23 March 2016; Accepted 17 May 2016

Academic Editor: Ricardo Weder

Copyright © 2016 Hongfang Li and Feng Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Cauchy problem for Laplace equation in a strip is considered. The optimal error bounds between the exact solution and its regularized approximation are given, which depend on the noise level either in a Hölder continuous way or in a logarithmic continuous way. We also provide two special regularization methods, that is, the generalized Tikhonov regularization and the generalized singular value decomposition, which realize the optimal error bounds.