Volume 42, pp. 136-146, 2014.

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

ETNA articles which cite this article

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

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