Transactions of Nanjing University of Aeronautics & Astronautics
Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems
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Abstract:
It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems, so fractional Tikhonov methods have been introduced to remedy this shortcoming. And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Arnoldi decomposition of the given matrix. In this paper, we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process. The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators. A suitable value of the regularization parameter is determined by the discrepancy principle. Numerical examples with application to image restoration are carried out to examine that the performance of the method.
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This work was supported by the National Natural Science Foundations of China (Nos.11571171 and 61473148).
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