Fourier Spectral Method for Analytic Continuation

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

• Zhenyu Zhao
• Lei You

• Analytic continuation
• ill-posed problem
• regularization method Fourier spectral method
• the discrepancy principle.

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