## R$^3$GMRES: Including Prior Information in GMRES-Type Methods for Discrete Inverse Problems

Yiqiu Dong, Henrik Garde, and Per Christian Hansen

### Abstract

Lothar Reichel and his collaborators proposed several iterative algorithms that augment the underlying Krylov subspace with an additional low-dimensional subspace in order to produce improved regularized solutions. We take a closer look at this approach and investigate a particular Regularized Range-Restricted GMRES method, R$^3$GMRES, with a subspace that represents prior information about the solution. We discuss the implementation of this approach and demonstrate its advantage by means of several test problems.

Full Text (PDF) [181 KB], BibTeX

### Key words

inverse problems, regularizing iterations, large-scale problems, prior information

65F22, 65F10