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Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle

In: Optimization and Regularization for Computational Inverse Problems and Applications

Author

Listed:
  • Hui Cao

    (Austrian Academy of Science, Johann Radon Institute for Computational and Applied Mathematics (RICAM))

  • Sergei Pereverzyev

    (Austrian Academy of Science, Johann Radon Institute for Computational and Applied Mathematics (RICAM))

Abstract

The chapter is a survey on recently proposed technique for parameter identification in partial differential equations. This technique combines natural linearization of an identification problem with the Tikhonov scheme, where the regularization parameter is chosen adaptively by means of the so-called balancing principle. We describe the natural linearization approach and show how it can be treated within the framework of Tikhonov regularization as a problem with noisy operator and noisy data. Then the balancing principle is discussed in the context of such a problem. We demonstrate the performance of proposed technique in some typical parameter identification problems.

Suggested Citation

  • Hui Cao & Sergei Pereverzyev, 2010. "Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle," Springer Books, in: Yanfei Wang & Changchun Yang & Anatoly G. Yagola (ed.), Optimization and Regularization for Computational Inverse Problems and Applications, chapter 0, pages 65-105, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-13742-6_4
    DOI: 10.1007/978-3-642-13742-6_4
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