Buchholz, P.Dayar, Tuğrul2016-02-082016-02-0820040024-3795http://hdl.handle.net/11693/27455Conference name: Conference on the Numerical Solution of Markov Chains 2003Date of Conference: 3-5 September 2003The Kronecker structure of a hierarchical Markovian model (HMM) induces nested block partitionings in the transition matrix of its underlying Markov chain. This paper shows how sparse real Schur factors of certain diagonal blocks of a given partitioning induced by the Kronecker structure can be constructed from smaller component matrices and their real Schur factors. Furthermore, it shows how the column approximate minimum degree (COLAMD) ordering algorithm can be used to reduce fill-in of the remaining diagonal blocks that are sparse LU factorized. Combining these ideas, the paper proposes three-level block successive over-relaxation (BSOR) as a competitive steady state solver for HMMs. Finally, on a set of numerical experiments it demonstrates how these ideas reduce storage required by the factors of the diagonal blocks and improve solution time compared to an all LU factorization implementation of the BSOR solver. © 2004 Elsevier Inc. All rights reserved.EnglishBlock SORCOLAMD orderingKronecker based numerical techniquesMarkov chainsReal Schur factorizationAlgorithmsApproximation theoryComputation theoryComputer simulationMathematical modelsMatrix algebraBlock SORCOLAMD orderingKronecker based numerical techniquesReal Schur factorizationMarkov processesConference Paper10.1016/j.laa.2003.12.017