An optimal filtering method for stable analytic continuation

In this paper, we consider the problem of numerical analytic continuation of an analytic function f (z) = f (x + iy) on a strip domain Omega(+) = {z = x + iy is an element of C | x is an element of R, 0 < y < y(0)}, where the data is given approximately only on the real axis y = 0. This problem is severely ill-posed: the solution does not depend continuously on the given data. A novel method (filtering) is used to solve this problem and an optimal error estimate with Holder type is proved. Numerical examples show that this method works effectively. (C) 2011 Elsevier B.V. All rights reserved.