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Volumn 18, Issue 6, 2011, Pages 961-980

Fast multilevel methods for Markov chains

Author keywords

Markov chain; Multigrid; Multilevel aggregation; Over correction; Stationary probability vector

Indexed keywords


EID: 82455162418     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.800     Document Type: Article
Times cited : (13)

References (46)
  • 1
    • 0028428645 scopus 로고
    • A multi-level solution algorithm for steady-state Markov chains. Proceedings of the 1994 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems
    • Horton G, Leutenegger ST. A multi-level solution algorithm for steady-state Markov chains. Proceedings of the 1994 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, 1994; 191-200.
    • (1994) , pp. 191-200
    • Horton, G.1    Leutenegger, S.T.2
  • 2
    • 81555213049 scopus 로고    scopus 로고
    • On-the-fly adaptive smoothed aggregation multigrid for Markov chains
    • DOI: 10.1137/100799034.
    • Treister E, Yavneh I. On-the-fly adaptive smoothed aggregation multigrid for Markov chains. Accepted to SIAM Journal on Scientific Computing 2011. DOI: 10.1137/100799034.
    • (2011) Accepted to SIAM Journal on Scientific Computing
    • Treister, E.1    Yavneh, I.2
  • 5
    • 80051888041 scopus 로고    scopus 로고
    • Top-level acceleration of adaptive algebraic multilevel methods for steady-state solution to Markov chains
    • DOI: 10.1007/s10444-010-9168-x. Accepted [15 April 2010].
    • De Sterck H, Manteuffel T, Miller K, Sanders G. Top-level acceleration of adaptive algebraic multilevel methods for steady-state solution to Markov chains. Advances in Computational Mathematics 2010. DOI: 10.1007/s10444-010-9168-x. Accepted [15 April 2010].
    • (2010) Advances in Computational Mathematics
    • De Sterck, H.1    Manteuffel, T.2    Miller, K.3    Sanders, G.4
  • 6
    • 0008441139 scopus 로고
    • Numerical methods in Markov chain modeling
    • Philippe B, Saad Y, Stewart WJ. Numerical methods in Markov chain modeling. Operations Research 1992; 40(6):1156-1179.
    • (1992) Operations Research , vol.40 , Issue.6 , pp. 1156-1179
    • Philippe, B.1    Saad, Y.2    Stewart, W.J.3
  • 7
    • 82455192058 scopus 로고    scopus 로고
    • MARCA Models: A collection of markov chain models, August . Accessed date: [1 August 2008].
    • Stewart WJ. MARCA Models: A collection of markov chain models, August 2008. Accessed date: [1 August 2008].
    • (2008)
    • Stewart, W.J.1
  • 8
    • 82455192057 scopus 로고
    • On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains. Technical Report 94-44, ICASE
    • Leutenegger ST, Horton G. On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains. Technical Report 94-44, ICASE, 1994.
    • (1994)
    • Leutenegger, S.T.1    Horton, G.2
  • 9
    • 0346729186 scopus 로고
    • Numerical solution of large finite Markov chains by algebraic multigrid techniques
    • Stewart W (ed.). Kluwer: Boston
    • Krieger UR. Numerical solution of large finite Markov chains by algebraic multigrid techniques. In Computations with Markov Chains, Stewart W (ed.). Kluwer: Boston, 1995; 403-424.
    • (1995) Computations with Markov Chains , pp. 403-424
    • Krieger, U.R.1
  • 10
    • 82455170870 scopus 로고
    • A lumping method for numerical calculations of stationary distributions of Markov chains. Technical Report B-18, Department of Information Sciences, Tokyo Institute of Technology
    • Takahashi Y. A lumping method for numerical calculations of stationary distributions of Markov chains. Technical Report B-18, Department of Information Sciences, Tokyo Institute of Technology, 1975.
    • (1975)
    • Takahashi, Y.1
  • 11
    • 0001633546 scopus 로고
    • Aggregation of variables in dynamic systems
    • Simon HA, Ando A. Aggregation of variables in dynamic systems. Econometrica 1961; 29:111-138.
    • (1961) Econometrica , vol.29 , pp. 111-138
    • Simon, H.A.1    Ando, A.2
  • 12
  • 13
    • 0343638185 scopus 로고
    • A local convergence proof for the iterative aggregation method
    • Mandel J, Sekerka B. A local convergence proof for the iterative aggregation method. Linear Algebra and its Applications 1983; 51:163-172.
    • (1983) Linear Algebra and its Applications , vol.51 , pp. 163-172
    • Mandel, J.1    Sekerka, B.2
  • 14
    • 0000556573 scopus 로고
    • Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains
    • Koury JR, McAllister DF, Stewart WJ. Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains. SIAM Journal on Algebraic and Discrete Methods 1984; 5(2):164-186.
    • (1984) SIAM Journal on Algebraic and Discrete Methods , vol.5 , Issue.2 , pp. 164-186
    • Koury, J.R.1    McAllister, D.F.2    Stewart, W.J.3
  • 15
    • 0022093129 scopus 로고
    • Iterative aggregation/disaggregation techniques for nearly uncoupled Markov chains
    • Cao W-L, Stewart WJ. Iterative aggregation/disaggregation techniques for nearly uncoupled Markov chains. Journal of the ACM 1985; 32(3):702-719.
    • (1985) Journal of the ACM , vol.32 , Issue.3 , pp. 702-719
    • Cao, W.-L.1    Stewart, W.J.2
  • 16
    • 0023399469 scopus 로고
    • Aggregation/disaggregation methods for computing the stationary distribution of Markov chains
    • Haviv M. Aggregation/disaggregation methods for computing the stationary distribution of Markov chains. SIAM Journal on Numerical Analysis 1987; 24(4):952-966.
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , Issue.4 , pp. 952-966
    • Haviv, M.1
  • 17
    • 21844493797 scopus 로고
    • On a two-level multigrid solution method for Markov chains
    • Krieger UR. On a two-level multigrid solution method for Markov chains. Linear Algebra and its Applications 1995; 223-224:415-438.
    • (1995) Linear Algebra and its Applications , vol.223-224 , pp. 415-438
    • Krieger, U.R.1
  • 18
    • 0032344877 scopus 로고    scopus 로고
    • Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices
    • Marek I, Mayer P. Convergence analysis of an iterative aggregation/disaggregation method for computing stationary probability vectors of stochastic matrices. Numerical Linear Algebra with Applications 1998; 5:253-274.
    • (1998) Numerical Linear Algebra with Applications , vol.5 , pp. 253-274
    • Marek, I.1    Mayer, P.2
  • 19
    • 76049124858 scopus 로고    scopus 로고
    • Convergence theory of some classes of iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices
    • Marek I, Mayer P. Convergence theory of some classes of iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices. Linear Algebra and its Applications 2003; 363:177-200.
    • (2003) Linear Algebra and its Applications , vol.363 , pp. 177-200
    • Marek, I.1    Mayer, P.2
  • 20
    • 2942615438 scopus 로고    scopus 로고
    • Algebraic Schwarz methods for the numerical solution of Markov chains
    • Marek I, Szyld DB. Algebraic Schwarz methods for the numerical solution of Markov chains. Linear Algebra and its Applications 2004; 386:67-81.
    • (2004) Linear Algebra and its Applications , vol.386 , pp. 67-81
    • Marek, I.1    Szyld, D.B.2
  • 27
  • 28
    • 77949572841 scopus 로고    scopus 로고
    • Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methods
    • Seibold B. Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methods. Numerical Linear Algebra with Applications 2010; 17:433-451.
    • (2010) Numerical Linear Algebra with Applications , vol.17 , pp. 433-451
    • Seibold, B.1
  • 32
    • 0022131573 scopus 로고
    • Regenerative analysis and steady-state distributions for Markov chains
    • Grassmann W, Taksar M, Heyman D. Regenerative analysis and steady-state distributions for Markov chains. Operations Research 1985; 33(5):1107-1116.
    • (1985) Operations Research , vol.33 , Issue.5 , pp. 1107-1116
    • Grassmann, W.1    Taksar, M.2    Heyman, D.3
  • 36
    • 82455192054 scopus 로고    scopus 로고
    • Algebraic multigrid (amg): an introduction with applications. Technical Report 70, GMD - Forschungszentrum Informationstechnik GmbH
    • Klaus S. Algebraic multigrid (amg): an introduction with applications. Technical Report 70, GMD - Forschungszentrum Informationstechnik GmbH, 1999.
    • (1999)
    • Klaus, S.1
  • 37
    • 4243361725 scopus 로고
    • Modification of two-level algorithm with overcorrection
    • Vaněk P, Míka S. Modification of two-level algorithm with overcorrection. Applications of Mathematics 1992; 37:13-28.
    • (1992) Applications of Mathematics , vol.37 , pp. 13-28
    • Vaněk, P.1    Míka, S.2
  • 38
    • 38249029480 scopus 로고
    • A multilevel method with overcorrection by aggregation for solving discrete elliptic problems
    • Blaheta R. A multilevel method with overcorrection by aggregation for solving discrete elliptic problems. Journal of Computational and Applied Mathematics 1988; 24:227-239.
    • (1988) Journal of Computational and Applied Mathematics , vol.24 , pp. 227-239
    • Blaheta, R.1
  • 39
    • 0029488033 scopus 로고
    • Towards algebraic multigrid for elliptic problems of second order
    • Braess D. Towards algebraic multigrid for elliptic problems of second order. Computing 1995; 55:379-393.
    • (1995) Computing , vol.55 , pp. 379-393
    • Braess, D.1
  • 40
    • 0000221506 scopus 로고
    • Accelerated multigrid convergence and high-Reynolds recirculating flows
    • Brandt A, Yavneh I. Accelerated multigrid convergence and high-Reynolds recirculating flows. SIAM Journal on Scientific Computing 1993; 14(3):607-626.
    • (1993) SIAM Journal on Scientific Computing , vol.14 , Issue.3 , pp. 607-626
    • Brandt, A.1    Yavneh, I.2
  • 41
    • 82455170869 scopus 로고    scopus 로고
    • An aggregation multigrid solver for convection-diffusion problems on unstructured meshes. Technical Report UCD-CCM-130, University of Colorado at Denver
    • Guillard H, Vaněk P. An aggregation multigrid solver for convection-diffusion problems on unstructured meshes. Technical Report UCD-CCM-130, University of Colorado at Denver, 1998.
    • (1998)
    • Guillard, H.1    Vaněk, P.2
  • 42
    • 0013349686 scopus 로고    scopus 로고
    • Residual scaling techniques in multigrid, I: equivalence proof
    • Zhang J. Residual scaling techniques in multigrid, I: equivalence proof. Applied Mathematics and Computation 1997; 86:283-303.
    • (1997) Applied Mathematics and Computation , vol.86 , pp. 283-303
    • Zhang, J.1
  • 43
    • 0013395520 scopus 로고    scopus 로고
    • Residual scaling techniques in multigrid, II: practical applications
    • Zhang J. Residual scaling techniques in multigrid, II: practical applications. Applied Mathematics and Computation 1998; 90:229-252.
    • (1998) Applied Mathematics and Computation , vol.90 , pp. 229-252
    • Zhang, J.1
  • 44
    • 0040431745 scopus 로고    scopus 로고
    • Minimal residual smoothing in multi-level iterative method
    • Zhang J. Minimal residual smoothing in multi-level iterative method. Applied Mathematics and Computation 1997; 84:1-25.
    • (1997) Applied Mathematics and Computation , vol.84 , pp. 1-25
    • Zhang, J.1
  • 45
    • 0033709988 scopus 로고    scopus 로고
    • Comparison of partitioning techniques for two-level iterative solvers on large, sparse, Markov chains
    • Dayar T, Stewart WJ. Comparison of partitioning techniques for two-level iterative solvers on large, sparse, Markov chains. SIAM Journal on Scientific Computing 2000; 21:1691-1705.
    • (2000) SIAM Journal on Scientific Computing , vol.21 , pp. 1691-1705
    • Dayar, T.1    Stewart, W.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.