Geodesic
R$^3$GMRES: including prior information in GMRES-type methods for discrete inverse problems
Electronic transactions on numerical analysis, Tome 42 (2014), pp. 136-146.

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Summary: 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.
Classification : 65F22, 65F10
Keywords: inverse problems, regularizing iterations, large-scale problems, prior information 
@article{ETNA_2014__42__a3,
     author = {Dong, Yiqiu and Garde, Henrik and Hansen, Per Christian},
     title = {R$^3${GMRES:} including prior information in {GMRES-type} methods for discrete inverse problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {136--146},
     publisher = {mathdoc},
     volume = {42},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__42__a3/}
}
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Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian. R$^3$GMRES: including prior information in GMRES-type methods for discrete inverse problems. Electronic transactions on numerical analysis, Tome 42 (2014), pp. 136-146. http://geodesic.mathdoc.fr/item/ETNA_2014__42__a3/