A mollification regularization method for stable analytic continuation

作者:Deng, Zhi-Liang; Fu, Chu-Li*; Feng, Xiao-Li; Zhang, Yuan-Xiang
来源:Mathematics and Computers in Simulation, 2011, 81(8): 1593-1608.
DOI:10.1016/j.matcom.2010.11.011

摘要

In this paper. we consider an analytic continuation problem on a strip domain with the data given approximately only on the real axis. The Gauss mollification method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, we also propose a new a posteriori parameter choice rule and get a good error estimate. Several numerical examples are provided, which show the method works effectively.