Geodesic
On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning
Electronic transactions on numerical analysis, Tome 12 (2001), pp. 88-112
Parallel two-stage iterative methods for the solution of linear systems are analyzed. Convergence properties of both block and multisplitting two-stage methods are investigated either when the number of inner iterations becomes sufficiently large or when the matrix of the linear system is Hermitian positive definite. Comparison theorems for the parallel two-stage methods, based on the number of inner iterations performed, are given. Computational results of these methods on two parallel computing systems are included to illustrate the theoretical results.
Classification : 65F10, 65F15
Keywords: linear systems, two-stage methods, block methods, multisplitting methods, Hermitian matrix, positive definite matrix, preconditioners, parallel algorithms, monotonicity, distributed memory 
@article{ETNA_2001__12__a7,
     author = {Castel,  Jes\'us M. and Migall\'on,  Violeta and Penad\'es,  Jos\'e},
     title = {On parallel two-stage methods for {Hermitian} positive definite matrices with applications to preconditioning},
     journal = {Electronic transactions on numerical analysis},
     pages = {88--112},
     year = {2001},
     volume = {12},
     zbl = {0983.65042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2001__12__a7/}
}
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AU  - Migallón,  Violeta
AU  - Penadés,  José
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JO  - Electronic transactions on numerical analysis
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%0 Journal Article
%A Castel,  Jesús M.
%A Migallón,  Violeta
%A Penadés,  José
%T On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning
%J Electronic transactions on numerical analysis
%D 2001
%P 88-112
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%U http://geodesic.mathdoc.fr/item/ETNA_2001__12__a7/
%G en
%F ETNA_2001__12__a7
Castel,  Jesús M.; Migallón,  Violeta; Penadés,  José. On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning. Electronic transactions on numerical analysis, Tome 12 (2001), pp. 88-112. http://geodesic.mathdoc.fr/item/ETNA_2001__12__a7/