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A MODIFIED TIKHONOV REGULARIZATION FOR STABLE ANALYTIC CONTINUATION

CHU-LI FU, ZHI-LIANG DENG, XIAO-LI FENG and FANG-FANG DOU
SIAM Journal on Numerical Analysis
Vol. 47, No. 4 (2009), pp. 2982-3000
Stable URL: http://www.jstor.org/stable/27862762
Page Count: 19
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A MODIFIED TIKHONOV REGULARIZATION FOR STABLE ANALYTIC CONTINUATION
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Abstract

This paper is devoted to a new regularization method for solving the numerical analytic continuation of an analytic function f(z) = f(x +iy) on a strip domain Ω + = {z = x + iy ∈ C| x ∈ R, 0 < y < y0}, where the data is given approximately only on the line y = 0. This problem is severely ill-posed and has important practical applications. The theoretical optimal error bound for the problem is proved which is independent of the selected regularization methods. A modified Tikhonov regularization method with asymptotic order optimal error estimates is proposed. This method can be numerically implemented easily by the fast Fourier transform. Some numerical examples are provided and a comparison with a Fourier regularization method is given, which show the modified Tikhonov method works very well.

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