A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Abstract

In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.