Optimal Stable Approximation for the Cauchy Problem for Laplace Equation

Hongfang Li and Feng Zhou

Advances in Mathematical Physics, 2016, vol. 2016, issue 1

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.

Date: 2016
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https://doi.org/10.1155/2016/1468634

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:1468634

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