Geodesic
A quadratically convergent Bernoulli-like algorithm for solving matrix polynomial equations in Markov chains
Electronic transactions on numerical analysis, Tome 17 (2004), pp. 151-167.

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

Summary: A quadratically convergent algorithm is developed for solving matrix polynomial equations arising in M/G/1 and G/M/1 type Markov chains. The algorithm is based on the computation of generalized block eigenvalues/vectors of a suitable pair of matrices by means of a Bernoulli-like method. The use of the displacement structure allows one to reduce the computational cost per step. A shifting technique speeds up the rate of convergence.
Classification : 15A24, 60J22, 65F15
Keywords: polynomial matrix equations, Markov chains, generalized eigenvalues/eigenvectors, displacement structure 
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     author = {He, C. and Meini, B. and Rhee, N.H. and Sohraby, K.},
     title = {A quadratically convergent {Bernoulli-like} algorithm for solving matrix polynomial equations in {Markov} chains},
     journal = {Electronic transactions on numerical analysis},
     pages = {151--167},
     publisher = {mathdoc},
     volume = {17},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__17__a5/}
}
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He, C.; Meini, B.; Rhee, N.H.; Sohraby, K. A quadratically convergent Bernoulli-like algorithm for solving matrix polynomial equations in Markov chains. Electronic transactions on numerical analysis, Tome 17 (2004), pp. 151-167. http://geodesic.mathdoc.fr/item/ETNA_2004__17__a5/