A fractional Landweber iterative regularization method for stable analytic continuation

Fan Yang; Qianchao Wang; Xiaoxiao Li; Fan Yang; Qianchao Wang; Xiaoxiao Li

doi:10.3934/math.2021025

AIMS Mathematics

2021, Volume 6, Issue 1: 404-419. doi: 10.3934/math.2021025

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Research article

A fractional Landweber iterative regularization method for stable analytic continuation

School of Science, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People's Republic of China

Received: 15 July 2020 Accepted: 14 September 2020 Published: 15 October 2020
MSC : 35R25, 35R30, 47A52

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.
- stable analytic continuation,
- fractional Landweber regularization method,
- Ill-posed problem,
- inverse problem
Citation: Fan Yang, Qianchao Wang, Xiaoxiao Li. A fractional Landweber iterative regularization method for stable analytic continuation[J]. AIMS Mathematics, 2021, 6(1): 404-419. doi: 10.3934/math.2021025

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Abstract

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.

References

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