Journal
APPLIED NUMERICAL MATHEMATICS
Volume 122, Issue -, Pages 108-128Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2017.08.004
Keywords
Weighted least squares functional; Gradient flow equation; Landweber iteration; Error estimates; Image deblurring
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Funding
- Natural Science Foundation of China [11661072]
- Natural Science Foundation of Gansu Province [145RJZA037]
- Doctoral Foundation of Northwest Normal University, China [5002-577]
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In this paper, we study a modified Landweber iteration method via a gradient flow equation induced by a weighted least squares functional. We investigate the proposed scheme for solving ill-posed problems under the setting of compact operator and pseudo differential operator. The a-priori and the a-posteriori choice rules for regularization parameters are given and both rules yield the order optimal error estimates. Relative to the classical Landweber method, the new method significantly reduces the number of iterations needed to match an appropriate stopping criterion. As applications, we focus on some important ill-posed problems arising from mathematical physics. Numerical experiments are conducted for showing the validity of the scheme. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
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