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Extrapolation Techniques of Tikhonov Regularization

In: Optimization and Regularization for Computational Inverse Problems and Applications

Author

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  • Tingyan Xiao

    (Hebei University of Technology, School of Sciences)

  • Yuan Zhao

    (Hebei University of Technology, School of Sciences)

  • Guozhong Su

    (Hebei University of Technology, School of Sciences)

Abstract

The numerical solution of inverse problems using Tikhonov’s regularization methods requires a huge amount of computations in iterative processes. It can employ extrapolation techniques to accelerate the convergence process or to improve accuracy of the regularized solution. This chapter aims to introduce some main extrapolation methods that have been studied for solving linear inverse problems in detail. Our emphasis is to discuss related technical problems, to propose a new extrapolation algorithm based on the Hermitian interpolation and to present results of numerical experiments for showing the merits of extrapolated regularization methods.

Suggested Citation

  • Tingyan Xiao & Yuan Zhao & Guozhong Su, 2010. "Extrapolation Techniques of Tikhonov Regularization," Springer Books, in: Yanfei Wang & Changchun Yang & Anatoly G. Yagola (ed.), Optimization and Regularization for Computational Inverse Problems and Applications, chapter 0, pages 107-126, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-13742-6_5
    DOI: 10.1007/978-3-642-13742-6_5
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