Geodesic
Preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks
Electronic transactions on numerical analysis, Tome 22 (2006), pp. 114-121
We introduce a new preconditioning technique for the iterative solution of saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioners are block diagonal and are based on augmentation, using symmetric positive definite weight matrices. If the nullity is equal to the number of constraints, the preconditioned matrices have precisely two distinct eigenvalues, giving rise to immediate convergence of preconditioned MINRES. Numerical examples illustrate our analytical findings.
Classification : 65F10
Keywords: saddle point linear systems, high nullity, augmentation, block diagonal preconditioners, Krylov subspace iterative solvers 
@article{ETNA_2006__22__a3,
     author = {Greif,  Chen and Sch\"otzau,  Dominik},
     title = {Preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks},
     journal = {Electronic transactions on numerical analysis},
     pages = {114--121},
     year = {2006},
     volume = {22},
     zbl = {1112.65042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__22__a3/}
}
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Greif,  Chen; Schötzau,  Dominik. Preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks. Electronic transactions on numerical analysis, Tome 22 (2006), pp. 114-121. http://geodesic.mathdoc.fr/item/ETNA_2006__22__a3/