Approximate inverse method for stable analytic continuation in a strip domain

Abstract

Numerical analytic continuation is, in general, an ill-posed problem and some special regularization methods are needed. In this paper we apply the approximate inverse method to deal with the problem in a strip domain Ω = { z = x + i y ∈ C ∣ x ∈ R , 0 < ∣ y ∣ < y 0 } in complex plane, the data is known approximately only on the line y = 0 . Error estimate between the exact and approximate solution with regularization parameter selected by both a priori and a posteriori strategy are provided, respectively. Numerical results show that the method works effectively, and can be a competitive alternative to existing method for the problem.