Geodesic
On preconditioning Schur complement and Schur complement preconditioning
Electronic transactions on numerical analysis, Tome 10 (2000), pp. 115-130
We study two implementation strategies to utilize Schur complement technique in multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. The first strategy constructs a RILUM to precondition the original matrix. The second strategy solves the first Schur complement matrix using the lower level parts of the RILUM as the preconditioner. We discuss computational and memory costs of both strategies and the potential effect on grid independent convergence rate of RILUM with different implementation strategies.
Classification : 65F10, 65N06
Keywords: sparse matrices, Schur complement, RILUM, preconditioning techniques 
@article{ETNA_2000__10__a0,
     author = {Zhang,  Jun},
     title = {On preconditioning {Schur} complement and {Schur} complement preconditioning},
     journal = {Electronic transactions on numerical analysis},
     pages = {115--130},
     year = {2000},
     volume = {10},
     zbl = {0951.65042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2000__10__a0/}
}
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AU  - Zhang,  Jun
TI  - On preconditioning Schur complement and Schur complement preconditioning
JO  - Electronic transactions on numerical analysis
PY  - 2000
SP  - 115
EP  - 130
VL  - 10
UR  - http://geodesic.mathdoc.fr/item/ETNA_2000__10__a0/
LA  - en
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%0 Journal Article
%A Zhang,  Jun
%T On preconditioning Schur complement and Schur complement preconditioning
%J Electronic transactions on numerical analysis
%D 2000
%P 115-130
%V 10
%U http://geodesic.mathdoc.fr/item/ETNA_2000__10__a0/
%G en
%F ETNA_2000__10__a0
Zhang,  Jun. On preconditioning Schur complement and Schur complement preconditioning. Electronic transactions on numerical analysis, Tome 10 (2000), pp. 115-130. http://geodesic.mathdoc.fr/item/ETNA_2000__10__a0/