Geodesic
Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems
Electronic transactions on numerical analysis, Tome 29 (2008)
In this paper we analyze the smoothing property from classical Algebraic Multigrid theory, for general rectangular systems of linear equations. We prove it for Kaczmarz's projection algorithm in the consistent case and obtain in this way a generalization of the classical well-known result by A. Brandt. We then extend this result for the Kaczmarz Extended algorithm in the inconsistent case.
Classification : 65F10, 65F20, 65N55
Keywords: algebraic multigrid, smoothing property, kaczmarz relaxation, inconsistent least squares problems 
@article{ETNA_2008__29__a4,
     author = {Popa,  Constantin},
     title = {Algebraic multigrid smoothing property of {Kaczmarz's} relaxation for general rectangular linear systems},
     journal = {Electronic transactions on numerical analysis},
     year = {2008},
     volume = {29},
     zbl = {1188.65036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a4/}
}
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AU  - Popa,  Constantin
TI  - Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems
JO  - Electronic transactions on numerical analysis
PY  - 2008
VL  - 29
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__29__a4/
LA  - en
ID  - ETNA_2008__29__a4
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%0 Journal Article
%A Popa,  Constantin
%T Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems
%J Electronic transactions on numerical analysis
%D 2008
%V 29
%U http://geodesic.mathdoc.fr/item/ETNA_2008__29__a4/
%G en
%F ETNA_2008__29__a4
Popa,  Constantin. Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a4/