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Volumn 288, Issue 1-3, 1999, Pages 175-186

On the numerical solution of a nonlinear matrix equation in Markov chains

Author keywords

Convergence rate; Iterative methods; Markov chains; Matrix equation

Indexed keywords


EID: 0040219762     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)10190-8     Document Type: Article
Times cited : (12)

References (14)
  • 1
    • 21944447710 scopus 로고    scopus 로고
    • A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains
    • Z.-Z. Bai, A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains, Linear Algebra Appl. 266 (1997) 219-241.
    • (1997) Linear Algebra Appl. , vol.266 , pp. 219-241
    • Bai, Z.-Z.1
  • 2
    • 0030492130 scopus 로고    scopus 로고
    • On the solution of a nonlinear matrix equation arising in queueing problems
    • D. Bini, B. Meini, On the solution of a nonlinear matrix equation arising in queueing problems, SIAM J. Matrix Anal. Appl. 17 (1996) 906-926.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 906-926
    • Bini, D.1    Meini, B.2
  • 6
    • 21844506405 scopus 로고
    • Newton's iteration for non-linear equations in Markov chains
    • G. Latouche, Newton's iteration for non-linear equations in Markov chains, IMA J. Numer. Anal. 14 (1994) 583-598.
    • (1994) IMA J. Numer. Anal. , vol.14 , pp. 583-598
    • Latouche, G.1
  • 7
    • 0009930241 scopus 로고
    • Algorithms for evaluating the matrix G in Markov chains of PH/G/1 type
    • G. Latouche, Algorithms for evaluating the matrix G in Markov chains of PH/G/1 type, Cahiers Centre Études Rech. Opér. 36 (1994) 251-258.
    • (1994) Cahiers Centre Études Rech. Opér. , vol.36 , pp. 251-258
    • Latouche, G.1
  • 8
    • 0031321618 scopus 로고    scopus 로고
    • New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains
    • B. Meini, New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains, Numer. Math. 78 (1997) 39-58.
    • (1997) Numer. Math. , vol.78 , pp. 39-58
    • Meini, B.1
  • 9
    • 0009924724 scopus 로고
    • Moment formulas for the Markov renewal branching process
    • M.F. Neuts, Moment formulas for the Markov renewal branching process, Adv. in Appl. Probab. 8 (1976) 690-711.
    • (1976) Adv. in Appl. Probab. , vol.8 , pp. 690-711
    • Neuts, M.F.1
  • 10
    • 0018493259 scopus 로고
    • Queues solvable without Rouche's theorem
    • M.F. Neuts, Queues solvable without Rouche's theorem, Oper. Res. 27 (1979) 767-781.
    • (1979) Oper. Res. , vol.27 , pp. 767-781
    • Neuts, M.F.1
  • 12
    • 0024018936 scopus 로고
    • Nonlinear matrix equations in applied probability - Solution techniques and open problems
    • V. Ramaswami, Nonlinear matrix equations in applied probability - solution techniques and open problems, SIAM Rev. 30 (1988) 256-263.
    • (1988) SIAM Rev. , vol.30 , pp. 256-263
    • Ramaswami, V.1
  • 13
    • 84968508605 scopus 로고
    • A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces
    • W.C. Rheinboldt, J.S. Vandergraft, A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces, Math. Comp. 27 (1973) 139-145.
    • (1973) Math. Comp. , vol.27 , pp. 139-145
    • Rheinboldt, W.C.1    Vandergraft, J.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.