Lanczos-Based Exponential Filtering for Discrete Ill-Posed Problems

We describe regularizing iterative methods for the solution of large ill-conditioned linear systems of equations that arise from the discretization of linear ill-posed problems. The regularization is specified by a filter function of Gaussian type. A parameter μ determines the amount of regularization applied. The iterative methods are based on a truncated Lanczos decomposition and the filter function is approximated by a linear combination of Lanczos polynomials. A suitable value of the regularization parameter is determined by an L-curve criterion. Computed examples that illustrate the performance of the methods are presented.