Geodesic
An implicit approximate inverse preconditioner for saddle point problems
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 173-188
We present a preconditioner for saddle point problems which is based on an approximation of an implicit representation of the inverse of the saddle point matrix. Whereas this preconditioner does not require an approximation to the Schur complement, its theoretical analysis yields some interesting relationship to some Schurcomplement-based preconditioners. Whereas the evaluation of this new preconditioner is slightly more expensive than the evaluation of standard block preconditioners from the literature, it has the advantage that, similar to constraint preconditioners, the iterates of the preconditioned system satisfy the constraint equations exactly. We will demonstrate the performance of the implicit approximate inverse preconditioner in the iterative solution of the discrete twoas well as three-dimensional Oseen equations.
Classification : 65F05, 65F30, 65F50, 65N22, 65N30
Keywords: saddle point problem, preconditioning 
@article{ETNA_2010__37__a15,
     author = {Le Borne,  Sabine and Ngufor,  Che},
     title = {An implicit approximate inverse preconditioner for saddle point problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {173--188},
     year = {2010},
     volume = {37},
     zbl = {1205.65140},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a15/}
}
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AU  - Ngufor,  Che
TI  - An implicit approximate inverse preconditioner for saddle point problems
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SP  - 173
EP  - 188
VL  - 37
UR  - http://geodesic.mathdoc.fr/item/ETNA_2010__37__a15/
LA  - en
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%A Le Borne,  Sabine
%A Ngufor,  Che
%T An implicit approximate inverse preconditioner for saddle point problems
%J Electronic transactions on numerical analysis
%D 2010
%P 173-188
%V 37
%U http://geodesic.mathdoc.fr/item/ETNA_2010__37__a15/
%G en
%F ETNA_2010__37__a15
Le Borne,  Sabine; Ngufor,  Che. An implicit approximate inverse preconditioner for saddle point problems. Electronic transactions on numerical analysis, Tome 37 (2010), pp. 173-188. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a15/