A simple regularization method for stable analytic continuation**The project is supported by the National Natural Science Foundation of China (Nos. 10671085, 10571079 and 10726017).

Abstract

The problems of analytic continuation are frequently encountered in many practical applications. These problems are well known to be severely ill-posed and therefore several regularization methods have been suggested for solving them. In this paper we consider the problem of analytic continuation of the analytic function f(z) = f(x + iy) on a strip domain , where the data are given only on the line y = 0. We use a very simple and convenient method—the Fourier regularization method to solve this problem. Some sharp error estimates between the exact solution and its approximation are given and numerical examples show the method works effectively.