Abstract
In this paper, we apply the multilevel augmentation method for solving ill-posed Fredholm integral equations of the first kind via iterated Tikhonov regularization method. The method leads to fast solutions of the discrete regularization methods for the equations. The convergence rates of iterated Tikhonov regularization are achieved by using a modified parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11761010
Award Identifier / Grant number: 11361005
Award Identifier / Grant number: 61502107
Award Identifier / Grant number: 11661008
Award Identifier / Grant number: 61863001
Funding source: Natural Science Foundation of Jiangxi Province
Award Identifier / Grant number: 20181BAB202021
Funding statement: Supported in part by the Natural Science Foundation of China under grants 11761010, 11361005, 61863001 and 11661008, and Natural Science Foundation of Jiangxi, China under grant 20181BAB202021.
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