Augmented Arnoldi-Tikhonov Regularization Methods for Solving Large-Scale Linear Ill-Posed Systems

Abstract EN

We propose an augmented Arnoldi-Tikhonov regularization method for the solution of large-scale linear ill-posed systems.

This method augments the Krylov subspace by a user-supplied low-dimensional subspace, which contains a rough approximation of the desired solution.

The augmentation is implemented by a modified Arnoldi process.

Some useful results are also presented.

Numerical experiments illustrate that the augmented method outperforms the corresponding method without augmentation on some real-world examples.