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.