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Modified Regularization Scheme with Application in Reconstructing Neumann-Dirichlet Mapping

In: Optimization and Regularization for Computational Inverse Problems and Applications

Author

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  • Pingli Xie

    (Henan University of Technology, School of Sciences)

  • Jin Cheng

    (Fudan University, School of Mathematical Sciences)

Abstract

In this chapter, we propose a new regularization method for solving a linear operator equation when the operator and right hand term are both known approximately. The advantage of our method is that we just use the information about the error level instead of assuming the reliable bounds of the unknown solution. The algorithms are presented and the numerical simulation results show the efficiency of our method. As an application, we discuss the problem of reconstructing the Neumann-Dirichlet mapping from the discrete Neumann and Dirichlet data. The Neumann-Dirichlet mappings are used widely in the studying of inverse problems for partial differential equations.

Suggested Citation

  • Pingli Xie & Jin Cheng, 2010. "Modified Regularization Scheme with Application in Reconstructing Neumann-Dirichlet Mapping," Springer Books, in: Yanfei Wang & Changchun Yang & Anatoly G. Yagola (ed.), Optimization and Regularization for Computational Inverse Problems and Applications, chapter 0, pages 127-138, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-13742-6_6
    DOI: 10.1007/978-3-642-13742-6_6
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