A MODIFIED TIKHONOV REGULARIZATION FOR STABLE ANALYTIC CONTINUATION

This paper is devoted to a new regularization method for solving the 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 vertical bar x is an element of R, 0 < y < y(0)}, where the data is given approximately only on the line y = 0. This problem is severely ill-posed and has important practical applications. The theoretical optimal error bound for the problem is proved which is independent of the selected regularization methods. A modified Tikhonov regularization method with asymptotic order optimal error estimates is proposed. This method can be numerically implemented easily by the fast Fourier transform. Some numerical examples are provided and a comparison with a Fourier regularization method is given, which show the modified Tikhonov method works very well.