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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. Mittal, Gaurav, 2024. "Nonstationary iterated frozen Tikhonov regularization with uniformly convex penalty terms for solving inverse problems," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    3. 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.
    4. 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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