Two Tikhonov‐type regularization methods for inverse source problem on the Poisson equation | Zendy

Zhao Jingjun | Zendy; Liu Songshu | Zendy; Liu Tao | Zendy

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Two Tikhonov‐type regularization methods for inverse source problem on the Poisson equation

Author(s) -

Zhao Jingjun,

Liu Songshu,

Liu Tao

Publication year - 2012

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.2693

Subject(s) - tikhonov regularization , backus–gilbert method , mathematics , regularization (linguistics) , regularization perspectives on support vector machines , inverse problem , a priori and a posteriori , poisson distribution , mathematical analysis , mathematical optimization , computer science , statistics , artificial intelligence , philosophy , epistemology

In this paper, we investigate a problem of the identification of an unknown source on Poisson equation from some fixed location. A conditional stability estimate for an inverse heat source problem is proved. We show that such a problem is mildly ill‐posed and further present two Tikhonov‐type regularization methods (a generalized Tikhonov regularization method and a simplified generalized Tikhonov regularization method) to deal with this problem. Convergence estimates are presented under the a priori choice of the regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of our methods. Copyright © 2012 John Wiley & Sons, Ltd.

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