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
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 
@article{ETNA_2004__17__a5,
     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},
     year = {2004},
     volume = {17},
     zbl = {1065.65006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__17__a5/}
}
TY  - JOUR
AU  - He,  C.
AU  - Meini,  B.
AU  - Rhee,  N.H.
AU  - Sohraby,  K.
TI  - A quadratically convergent Bernoulli-like algorithm for solving matrix polynomial equations in Markov chains
JO  - Electronic transactions on numerical analysis
PY  - 2004
SP  - 151
EP  - 167
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__17__a5/
LA  - en
ID  - ETNA_2004__17__a5
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%0 Journal Article
%A He,  C.
%A Meini,  B.
%A Rhee,  N.H.
%A Sohraby,  K.
%T A quadratically convergent Bernoulli-like algorithm for solving matrix polynomial equations in Markov chains
%J Electronic transactions on numerical analysis
%D 2004
%P 151-167
%V 17
%U http://geodesic.mathdoc.fr/item/ETNA_2004__17__a5/
%G en
%F ETNA_2004__17__a5
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/