Xiao-Li Feng

A simple regularization method for stable analytic continuation

The problems of analytic continuation are frequently encountered in many practical applications. These problems are well known to be severely ill-posed and therefore several regularization methods have been suggested for solving them. In this paper we consider the problem of analytic continuation of the analytic function f(z) = f(x + iy) on a strip domain , where the data are given only on the line y = 0. We use a very simple and convenient method—the Fourier regularization method to solve this problem. Some sharp error estimates between the exact solution and its approximation are given and numerical examples show the method works effectively.

Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region

In this paper we consider a numerical approximation of solution of nonhomogeneous backward heat conduction problem (BHCP) in bounded region based on Tikhonov regularization method. Error estimate at t=0 for this method is provided. According to the error estimate, a selection of regularization parameter is given. Meanwhile, a numerical implementation is described and the numerical results show that our algorithm is effective.

A modified method for high order numerical derivatives

In this paper we propose a new regularization method for computing high order numerical derivatives from one dimensional noisy data. The convergence estimate under an appropriate choice of the regularization parameter is obtained. Some interesting numerical tests show that the proposed method is effective and stable.

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

Determining surface heat flux in the steady state for the Cauchy problem for the Laplace equation

f(z)=f(x+iy)

A mollification regularization method for the Cauchy problem of an elliptic equation in a multi-dimensional case

on a strip domain

Stability and regularization of a backward parabolic PDE with variable coefficients

\Omega^+=\{z=x+iy\in \mathbb{C}\mid x\in \mathbb{R}, 0<y<y_0\}

Original article: A mollification regularization method for stable analytic continuation

, where the data is given approximately only on the line

A wavelet regularization method for solving numerical analytic continuation

y=0

A Quasi-Boundary-Value method for a Cauchy problem of an elliptic equation in multiple dimensions

. 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.