A fractional Landweber iterative regularization method for stable analytic continuation

In this paper, we consider the problem of analytic continuation of the analytic function $g(z) = g(x+iy)$ on a strip domain Ω = $\{z = x+iy\in \mathbb{C}|\, x\in\mathbb{R}, 0 < y < y_0\}$, where the data is given only on the line $y = 0$. This problem is a severely ill-posed problem. We propos...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 1; pp. 404 - 419
Main Authors Yang, Fan, Wang, Qianchao, Li, Xiaoxiao
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
fractional landweber regularization method
ill-posed problem
inverse problem
stable analytic continuation
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021025

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Summary:In this paper, we consider the problem of analytic continuation of the analytic function $g(z) = g(x+iy)$ on a strip domain Ω = $\{z = x+iy\in \mathbb{C}|\, x\in\mathbb{R}, 0 < y < y_0\}$, where the data is given only on the line $y = 0$. This problem is a severely ill-posed problem. We propose the fraction Landweber iterative regularization method to deal with this problem. Under the a priori and a posteriori regularization parameter choice rule, we all obtain the error estimates between the regularization solution and the exact solution. Some numerical examples are given to verify the efficiency and accuracy of the proposed methods.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021025