Geodesic
Block triangular preconditioners for $M$-matrices and Markov chains
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 209-227.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider preconditioned Krylov subspace methods for solving large sparse linear systems under the assumption that the coefficient matrix is a (possibly singular) -matrix. The matrices are partitioned into $$########$$§$$###$\ddot $###$$ block form using graph partitioning. Approximations to the Schur complement are used to produce various preconditioners of block triangular and block diagonal type. A few properties of the preconditioners are established, and extensive numerical experiments are used to illustrate the performance of the various preconditioners on singular linear systems arising from Markov modeling.
Classification : 05C50, 60J10, 60J22, 65F10, 65F35, 65F50
Keywords: -matrices, preconditioning, discrete Markov chains, iterative methods, graph partitioning $$###$$ 
@article{ETNA_2007__26__a14,
     author = {Benzi, Michele and U\c{c}ar, Bora},
     title = {Block triangular preconditioners for $M$-matrices and {Markov} chains},
     journal = {Electronic transactions on numerical analysis},
     pages = {209--227},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a14/}
}
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Benzi, Michele; Uçar, Bora. Block triangular preconditioners for $M$-matrices and Markov chains. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 209-227. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a14/