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Volumn 23, Issue 1, 2003, Pages 11-27

On a quadratic matrix equation associated with an M-matrix

Author keywords

Iterative methods; M matrices; Minimal non negative solution; Non symmetric algebraic Riccati equation; Quadratic matrix equation; Schur method; Stabilizing solution

Indexed keywords

ITERATIVE METHODS; MARKOV CHAINS; NUMERICAL METHODS; RICCATI EQUATIONS;

EID: 0037248874     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/23.1.11     Document Type: Article
Times cited : (29)

References (27)
  • 3
    • 43949169431 scopus 로고
    • On swapping diagonal blocks in real Schur form
    • BAI, Z. & DEMMEL, J. W. (1993) On swapping diagonal blocks in real Schur form. Linear Algebra Appl., 186, 73-95.
    • (1993) Linear Algebra Appl. , vol.186 , pp. 73-95
    • Bai, Z.1    Demmel, J.W.2
  • 5
    • 0032344706 scopus 로고    scopus 로고
    • A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils
    • BENNER, P., MEHRMANN, V. & Xu, H. (1998) A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils. Numer. Math., 78, 329-358.
    • (1998) Numer. Math. , vol.78 , pp. 329-358
    • Benner, P.1    Mehrmann, V.2    Xu, H.3
  • 7
    • 0000954153 scopus 로고
    • A Schur method for the square root of a matrix
    • BJÖRCK, A. & HAMMARLING, S. (1983) A Schur method for the square root of a matrix. Linear Algebra Appl., 52/53, 127-140.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 127-140
    • Björck, A.1    Hammarling, S.2
  • 8
    • 0001580828 scopus 로고
    • Singular perturbations of a general boundary value problem
    • CHANG, K. W. (1972) Singular perturbations of a general boundary value problem. SIAM J. Math. Anal., 3, 520-526.
    • (1972) SIAM J. Math. Anal. , vol.3 , pp. 520-526
    • Chang, K.W.1
  • 9
    • 0016971735 scopus 로고
    • Polynomial factorization via the Riccati equation
    • CLEMENTS, D. J. & ANDERSON, B. D. O. (1976) Polynomial factorization via the Riccati equation. SIAM J. Appl. Math., 31, 179-205.
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 179-205
    • Clements, D.J.1    Anderson, B.D.O.2
  • 11
    • 0036060733 scopus 로고    scopus 로고
    • Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices
    • GUO, C.-H. (2001) Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices. SIAM J. Matrix Anal. Appl., 23, 225-242.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 225-242
    • Guo, C.-H.1
  • 12
    • 85015357465 scopus 로고    scopus 로고
    • A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation
    • GUO, C.-H. (2002) A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation. Linear Algebra Appl., 357, 299-302.
    • (2002) Linear Algebra Appl. , vol.357 , pp. 299-302
    • Guo, C.-H.1
  • 13
    • 0032364897 scopus 로고    scopus 로고
    • Analysis and modification of Newton's method for algebraic Riccati equations
    • GUO, C.-H. & LANCASTER, P. (1998) Analysis and modification of Newton's method for algebraic Riccati equations. Math. Comp., 67, 1089-1105.
    • (1998) Math. Comp. , vol.67 , pp. 1089-1105
    • Guo, C.-H.1    Lancaster, P.2
  • 14
    • 0041410017 scopus 로고    scopus 로고
    • On the iterative solution of a class of nonsymmetric algebraic Riccati equations
    • GUO, C.-H. & LAUB, A. J. (2000) On the iterative solution of a class of nonsymmetric algebraic Riccati equations. SIAM J. Matrix Anal. Appl., 22, 376-391.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.22 , pp. 376-391
    • Guo, C.-H.1    Laub, A.J.2
  • 15
    • 0001485725 scopus 로고
    • Computing real square roots of a real matrix
    • HIGHAM, N. J. (1987) Computing real square roots of a real matrix. Linear Algebra Appl., 88/89, 405-430.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 405-430
    • Higham, N.J.1
  • 16
    • 0034288884 scopus 로고    scopus 로고
    • Numerical analysis of a quadratic matrix equation
    • HIGHAM, N. J. & KIM, H.-M. (2000) Numerical analysis of a quadratic matrix equation. IMA J. Numer. Anal., 20, 499-519.
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 499-519
    • Higham, N.J.1    Kim, H.-M.2
  • 17
    • 0032217347 scopus 로고    scopus 로고
    • Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices
    • JUANG, J. & LIN, W.-W. (1998) Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices. SIAM J. Matrix Anal. Appl., 20, 228-243.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 228-243
    • Juang, J.1    Lin, W.-W.2
  • 18
    • 0344843807 scopus 로고
    • Probabilistic factorization of a quadratic matrix polynomial
    • KENNEDY, J. & WILLIAMS, D. (1990) Probabilistic factorization of a quadratic matrix polynomial. Math. Proc. Cambridge Philos. Soc., 107, 591-600.
    • (1990) Math. Proc. Cambridge Philos. Soc. , vol.107 , pp. 591-600
    • Kennedy, J.1    Williams, D.2
  • 19
    • 0024719754 scopus 로고
    • Positive and negative solutions of dual Riccati equations by matrix sign function iteration
    • KENNY, C., LAUB, A. J. & JONCKHEERE, E. A. (1989a) Positive and negative solutions of dual Riccati equations by matrix sign function iteration. Systems Control Lett., 13, 109-116.
    • (1989) Systems Control Lett. , vol.13 , pp. 109-116
    • Kenny, C.1    Laub, A.J.2    Jonckheere, E.A.3
  • 20
    • 0024641418 scopus 로고
    • A stability-enhancing scaling procedure for Schur-Riccati solvers
    • KENNY, C., LAUB, A. J. & WETTE, M. (1989b) A stability-enhancing scaling procedure for Schur-Riccati solvers. Systems Control Lett., 12, 241-250.
    • (1989) Systems Control Lett. , vol.12 , pp. 241-250
    • Kenny, C.1    Laub, A.J.2    Wette, M.3
  • 22
    • 0018681625 scopus 로고
    • A Schur method for solving algebraic Riccati equations
    • LAUB, A. J. (1979) A Schur method for solving algebraic Riccati equations. IEEE Trans. Automat. Control, 24, 913-921.
    • (1979) IEEE Trans. Automat. Control , vol.24 , pp. 913-921
    • Laub, A.J.1
  • 23
    • 0031233599 scopus 로고    scopus 로고
    • Numerical improvements for solving Riccati equations
    • LAUB, A. J. & GAHINET, P. (1997) Numerical improvements for solving Riccati equations. IEEE Trans. Automat. Control, 42, 1303-1308.
    • (1997) IEEE Trans. Automat. Control , vol.42 , pp. 1303-1308
    • Laub, A.J.1    Gahinet, P.2
  • 24
    • 0016896171 scopus 로고
    • The matrix equation AZ + B - ZCZ - ZD = 0
    • MEYER, H.-B. (1976) The matrix equation AZ + B - ZCZ - ZD = 0. SIAM J. Appl. Math., 30, 136-142.
    • (1976) SIAM J. Appl. Math. , vol.30 , pp. 136-142
    • Meyer, H.-B.1
  • 25
    • 0000860220 scopus 로고
    • Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains
    • ROGERS, L. C. G. (1994) Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Ann. Appl. Probab., 4, 390-413.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 390-413
    • Rogers, L.C.G.1
  • 26
    • 21844497387 scopus 로고
    • Computing the invariant law of a fluid model
    • ROGERS, L. C. G. & SHI, Z. (1994) Computing the invariant law of a fluid model. J. Appl. Probab., 31, 885-896.
    • (1994) J. Appl. Probab. , vol.31 , pp. 885-896
    • Rogers, L.C.G.1    Shi, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.