A modified Lavrentiev iterative regularization method for analytic continuation

Abstract We consider the problem of numerical analytic continuation of an analytic function f ( z ) = f ( x + i y ) on a strip domain Ω + = { z = x + i y ∈ C | x ∈ R , 0 y y 0 } , where the data is given approximately only on the line y = 0 . This is a severely ill-posed problem. Motivated by the advantage of iterative methods for solving ill-posed problems, we propose a new modified iterative method to solve this problem under both a priori and a posteriori parameter choice rules. Moreover, some sharp error estimates between the exact solution and its approximation are proved. Some interesting numerical examples are conducted for showing that the newly-developed method works well.