AIMS Mathematics, 2021, 6(1): 404-419. doi: 10.3934/math.2021025 Research article

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A fractional Landweber iterative regularization method for stable analytic continuation

Fan Yang, Qianchao Wang, Xiaoxiao Li

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

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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.

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