A new second-order dynamical method for solving linear inverse problems in Hilbert spaces. (English) Zbl 07894882
Summary: 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.
MSC:
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 65R30 | Numerical methods for ill-posed problems for integral equations |
Software:
Regularization toolsReferences:
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