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A new second-order dynamical method for solving linear inverse problems in Hilbert spaces

Author

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  • Huang, Qin
  • Gong, Rongfang
  • Zhang, Ye

Abstract

A new second-order dynamic method (SODM) is proposed for solving ill-posed linear inverse problems in Hilbert spaces. The SODM can be viewed as a combination of Tikhonov regularization and second-order asymptotical regularization methods. As a result, a double-regularization-parameter strategy is adopted. The regularization properties of SODM are demonstrated under both a priori and a posteriori stopping rules. In the context of time discretization, we propose several iterative schemes with different choices of damping parameters. A truncated discrepancy principle is employed as the stop criterion. Finally, numerical experiments are performed to show the efficiency of the SODM: on the whole, compared with the classical Tikhonov method and the first-order dynamical-system method, the SODM leads to more-accurate approximate solutions while requiring fewer-iterative numbers.

Suggested Citation

  • Huang, Qin & Gong, Rongfang & Zhang, Ye, 2024. "A new second-order dynamical method for solving linear inverse problems in Hilbert spaces," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    • Handle: RePEc:eee:apmaco:v:473:y:2024:i:c:s0096300324001140
    DOI: 10.1016/j.amc.2024.128642
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