Transactions of Nanjing University of Aeronautics & Astronautics
A Preconditioned Fractional Tikhonov Regularization Method for Large Discrete Ill-posed Problems
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Abstract:
The generalized Tikhonov regularization method is one of the most classical methods for the solution of linear systems of equations that arise from the discretization of linear ill-posed problems. However， the approximate solution obtained by the Tikhonov regularization method in general form may lack many details of the exact solution. Combining the fractional Tikhonov method with the preconditioned technique， and using the discrepancy principle for determining the regularization parameter， we present a preconditioned projected fractional Tikhonov regularization method for solving discrete ill-posed problems. Numerical experiments illustrate that the proposed algorithm has higher accuracy compared with the existing classical regularization methods.
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Project Supported:
This work was supported in part by the National Natural Science Foundation of China （No.62073161） and the Fundamental Research Funds 2019 “Artificial Intelligence + Special Project” of Nanjing University of Aeronautics and Astronautics （No.2019009）.
Clc Number:
O241.6
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