Yuan-Xiang Zhang

The a posteriori Fourier method for solving ill-posed problems

The Fourier method is a rather effective and very simple regularization method for solving some ill-posed problems. The known works on this method are all limited to the a priori choice of the regularization parameter. In this paper, we will systematically consider the a posteriori choice of the regularization parameter, and the corresponding error estimates between the exact solution and its approximation are given. Numerical examples show the effectiveness of the a posteriori method, and the comparisons of the numerical effect between the a posteriori and the a priori Fourier methods are also taken into account.

An a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems

The goal of this paper is to investigate a backward parabolic equation with time-dependent coefficient by the truncation method (TM). The key point to our paper is that we give an a posteriori choice of regularization parameter for the TM, with which the convergence estimates between the exact solution and the regularized approximation are obtained. Numerical implementation sheds light on the accuracy and efficiency of the proposed method.

An iteration method for stable analytic continuation

Abstract In the present paper we consider the problem of numerical analytic continuation for an analytic function f ( z ) = f ( x + iy ) on a strip domain Ω + = { z = x + iy ∈ C | x ∈ R , 0 y y 0 } . The key difference with the known methods is that a novel iteration regularization method with a priori and a posteriori parameter choice rule is presented. The comparison in numerical aspect with other methods is also discussed.

Solving a backward heat conduction problem by variational method

Abstract The present paper is devoted to solve the backward heat conduction problem from the final temperature distribution. The problem is transformed into an optimization problem and then a variational method is given. A conjugate gradient method together with an appropriate stopping rule are used to solve this inverse problem. Several numerical examples are provided to show the high efficiency of the suggested method.

Approximate inverse method for stable analytic continuation in a strip domain

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 @W={z=x+iy@?C|x@?R,0<|y|