Fourier spectral method for analytic continuation
نویسندگان
چکیده
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. Keywords—analytic continuation,ill-posed problem, regularization method Fourier spectral method, the discrepancy principle
منابع مشابه
Supports of Functions and Integral Transforms
In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...
متن کاملVelocity continuation by spectral methods
I apply Fourier and Chebyshev spectral methods to derive accurate and efficient algorithms for velocity continuation. As expected, the accuracy of the spectral methods is noticeably superior to that of the finite-difference approach. Both methods apply a transformation of the time axis to squared time. The Chebyshev method is slightly less efficient than the Fourier method, but has less problem...
متن کاملDepth estimation of gravity anomalies by S-transform of analytic signal
The S-transform has widely been used in the analysis of non-stationary time series. A simple method to obtain depth estimates of gravity field sources is introduced in this study. We have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. This calculation procedure is based on replacement of the Fourier transform with the S-Tra...
متن کاملReal time quantum correlation functions. II. Maximum entropy numerical analytic continuation of path integral Monte Carlo and centroid molecular dynamics data
We propose a method which uses centroid molecular dynamics ~CMD! @J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 ~1994!# real-time data in conjunction with the imaginary-time data generated using path integral Monte Carlo simulations in a numerical analytic continuation scheme based on the maximum entropy approach. We show that significant improvement is achieved by including short-time CMD da...
متن کاملRecovering Exponential Accuracy in Fourier Spectral Methods Involving Piecewise Smooth Functions with Unbounded Derivative Singularities
Fourier spectral methods achieve exponential accuracy both on the approximation level and for solving partial differential equations (PDEs), if the solution is analytic. For linear PDEs with analytic but discontinuous solutions, Fourier spectral method produces poor pointwise accuracy, but still maintains exponential accuracy after post-processing [7]. In this paper, we develop a technique to r...
متن کامل