Abstract
In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.
Highlights
The problem of analytic continuation arises in many fields [1,2,3]
In order to better reconstruct the characteristics of exact solutions, we propose a fractional Tikhonov regularization method to solve Problem 1
Based on the above reasons, we will use the a posteriori fractional Tikhonov regularization method to study the analytical continuation problem mentioned at the beginning of the article
Summary
The problem of analytic continuation arises in many fields [1,2,3]. Medical imaging [4,5], the inversion of Laplace transform [6], inverse scattering problems [7], and so on. The analytical continuation problem is described as follows [8]
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