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

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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},
     year = {2007},
     volume = {26},
     zbl = {1171.65388},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a14/}
}
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%A Uçar,  Bora
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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/