Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4644857 | Applied Numerical Mathematics | 2016 | 14 Pages |
Abstract
In this paper, we consider a class of severely ill-posed backward problems for linear parabolic equations. We use a convolution regularization method to obtain a stable approximate initial data from the noisy final data. The convergence rates are obtained under an a priori and an a posteriori regularization parameter choice rule in which the a posteriori parameter choice is a new generalized discrepancy principle based on a modified version of Morozov's discrepancy principle. The log-type convergence order under the a priori regularization parameter choice rule and loglogloglog-type order under the a posteriori regularization parameter choice rule are obtained. Two numerical examples are tested to support our theoretical results.
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Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Cong Shi, Chen Wang, Ting Wei,