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Nonstationary Iterated Tikhonov Regularization

Author

Listed:
  • M. Hanke

    (Fachbereich Mathematik, Universität Kaiserslautern)

  • C. W. Groetsch

    (University of Cincinnati)

Abstract

A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. It is also shown that an order-optimal accuracy is attained when a certain a posteriori stopping rule is used to determine the iteration number.

Suggested Citation

  • M. Hanke & C. W. Groetsch, 1998. "Nonstationary Iterated Tikhonov Regularization," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 37-53, July.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:1:d:10.1023_a:1022680629327
    DOI: 10.1023/A:1022680629327
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    Cited by:

    1. Buccini, Alessandro & Park, Yonggi & Reichel, Lothar, 2018. "Numerical aspects of the nonstationary modified linearized Bregman algorithm," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 386-398.
    2. Reddy, G.D., 2019. "A class of parameter choice rules for stationary iterated weighted Tikhonov regularization scheme," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 464-476.
    3. Yan, Xiong-bin & Zhang, Zheng-qiang & Wei, Ting, 2022. "Simultaneous inversion of a time-dependent potential coefficient and a time source term in a time fractional diffusion-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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