## 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

### AMS subject classifications

65F22, 65F10

 Vol. 51 (2019), pp. 412-431 Andreas Neubauer: Augmented GMRES-type versus CGNE methods for the solution of linear ill-posed problems Vol. 55 (2022), pp. 341-364 Erin Carrier and Michael T. Heath: Exploiting compression in solving discretized linear systems Vol. 55 (2022), pp. 532-546 Kirk M. Soodhalter: A note on augmented unprojected Krylov subspace methods

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