Lanczos preconditioning of Lavrentiev regularization for discrete ill-posed problems

摘要

Tikhonov regularization is one of the most popular methods for solving large scale ill-posed linear systems. In the case of the linear operator is self-adjoint, the Tikhonov regularization method can be simplified to the method of Lavrentiev regularization. Preconditioning technique is used to make the linear system easier to solve by a given iterative method and accelerate the convergence. Lanczos based preconditioner is proposed recently by Rezghi and Hosseini. It is not limited only to special structured matrices. The Lavrentiev regularization can work much better when the Lanczos preconditioner is applied. Numerical experiments are given to demonstrate the effectiveness of the presented method.