메뉴 건너뛰기




Volumn 36, Issue 4, 1996, Pages 814-830

On the numerical solution of AX - XB = C

Author keywords

Arnoldi; Iterative methods; Krylov subspace; Matrix polynomials; Perturbation theory; Sylvester equation

Indexed keywords


EID: 0000844938     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01733793     Document Type: Article
Times cited : (49)

References (26)
  • 1
    • 84976855597 scopus 로고
    • Algorithm 432: Solution of the matrix equation AX + XB = C
    • R. H. Bartels and G. W. Stewart, Algorithm 432: Solution of the matrix equation AX + XB = C, Comm. ACM, 15 (1972), pp. 820-826.
    • (1972) Comm. ACM , vol.15 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 2
    • 51249161441 scopus 로고
    • Krylov space methods on state-space control models
    • D. L. Boley, Krylov space methods on state-space control models, Circ. Syst. & Signal Proc., 13 (1994), pp. 733-758.
    • (1994) Circ. Syst. & Signal Proc. , vol.13 , pp. 733-758
    • Boley, D.L.1
  • 4
    • 38249041276 scopus 로고
    • Computing stable eigendecomposition of matrices
    • J. Demmel, Computing stable eigendecomposition of matrices, Linear Algebra Appl., 79 (1986), pp. 163-193.
    • (1986) Linear Algebra Appl. , vol.79 , pp. 163-193
    • Demmel, J.1
  • 5
    • 0000875808 scopus 로고
    • Controllability, observability and the solution of AX - XB = C
    • E. de Souza and S. P. Bhattacharyya, Controllability, observability and the solution of AX - XB = C, Linear Algebra Appl., 39 (1981), pp. 167-188.
    • (1981) Linear Algebra Appl. , vol.39 , pp. 167-188
    • De Souza, E.1    Bhattacharyya, S.P.2
  • 6
    • 0001031880 scopus 로고
    • A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
    • R. W. Freund, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Cornput., 14 (1993), pp. 470-482.
    • (1993) SIAM J. Sci. Cornput. , vol.14 , pp. 470-482
    • Freund, R.W.1
  • 8
    • 0018721357 scopus 로고
    • A Hessenberg-Schur method for the problem AX + XB = C
    • G. H. Golub, S. Nash, and C. Van Loan, A Hessenberg-Schur method for the problem AX + XB = C, IEEE Trans. Autom. Contr., AC-24 (1979), pp. 909-913.
    • (1979) IEEE Trans. Autom. Contr. , vol.AC-24 , pp. 909-913
    • Golub, G.H.1    Nash, S.2    Van Loan, C.3
  • 9
    • 0015368704 scopus 로고
    • Resultants and the solution of AX - XB = -C
    • R. E. Hartwig, Resultants and the solution of AX - XB = -C, SIAM J. Appl. Math., 23 (1972), pp. 104-117.
    • (1972) SIAM J. Appl. Math. , vol.23 , pp. 104-117
    • Hartwig, R.E.1
  • 10
    • 0012031958 scopus 로고
    • Nonsingular solutions of TA - BT = C
    • J. Z. Hearon, Nonsingular solutions of TA - BT = C, Linear Algebra Appl., 16 (1977), pp. 57-63.
    • (1977) Linear Algebra Appl. , vol.16 , pp. 57-63
    • Hearon, J.Z.1
  • 11
    • 0001045175 scopus 로고
    • Perturbation theory and backward error for AX - XB = C
    • N. J. Higham, Perturbation theory and backward error for AX - XB = C, BIT, 33 (1993), pp. 124-136.
    • (1993) BIT , vol.33 , pp. 124-136
    • Higham, N.J.1
  • 12
    • 0003492388 scopus 로고
    • The Test Matrix Toolbox for Matlab
    • Manchester Centre for Computational Mathematics, University of Manchester, UK
    • N. J. Higham, The Test Matrix Toolbox for Matlab, Tech. Report 237, Manchester Centre for Computational Mathematics, University of Manchester, UK, 1993.
    • (1993) Tech. Report 237
    • Higham, N.J.1
  • 13
    • 21844518401 scopus 로고
    • Preconditioned Krylov subspace methods for Lyapunov matrix equations
    • M. Hochbruck and G. Starke, Preconditioned Krylov subspace methods for Lyapunov matrix equations, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 156-171.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 156-171
    • Hochbruck, M.1    Starke, G.2
  • 15
    • 38249011246 scopus 로고
    • Krylov subspace methods for the Sylvester equation
    • D. Y. Hu and L. Reichel, Krylov subspace methods for the Sylvester equation, Linear Algebra Appl., 174 (1992), pp. 283-314.
    • (1992) Linear Algebra Appl. , vol.174 , pp. 283-314
    • Hu, D.Y.1    Reichel, L.2
  • 16
    • 0028377922 scopus 로고
    • Krylov subspace methods for solving large Lyapunov equations
    • I. M. Jaimoukha and E. M. Kasenally, Krylov subspace methods for solving large Lyapunov equations, SIAM J. Numer. Anal., 31 (1994), pp. 227-251.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 227-251
    • Jaimoukha, I.M.1    Kasenally, E.M.2
  • 17
    • 0039616736 scopus 로고
    • A finite series solution of the matrix equation AX - XB = C
    • E. C. Ma, A finite series solution of the matrix equation AX - XB = C, J. SIAM Appl. Math, 14 (1966), pp. 490-495.
    • (1966) J. SIAM Appl. Math , vol.14 , pp. 490-495
    • Ma, E.C.1
  • 19
    • 0000253105 scopus 로고
    • Invariant description of linear, time-invariant controllable systems
    • V. M. Popov, Invariant description of linear, time-invariant controllable systems, SIAM J. Control, 10 (1972), pp. 252-264.
    • (1972) SIAM J. Control , vol.10 , pp. 252-264
    • Popov, V.M.1
  • 20
    • 0000175612 scopus 로고
    • Numerical solution of large Lyapunov equations
    • Signal Processing, Scattering, Operator Theory, and Numerical Methods. M. A. Kaashoek, J. H. van Schuppen, and A. C. Ran, eds., Boston, Birkhauser
    • Y. Saad, Numerical solution of large Lyapunov equations, in Signal Processing, Scattering, Operator Theory, and Numerical Methods. Proceedings of the international symposium MTNS-89, vol III, M. A. Kaashoek, J. H. van Schuppen, and A. C. Ran, eds., Boston, 1990, Birkhauser, pp. 503-511.
    • (1990) Proceedings of the International Symposium MTNS-89 , vol.3 , pp. 503-511
    • Saad, Y.1
  • 22
    • 1542603280 scopus 로고    scopus 로고
    • Arnoldi-Riccati method for large eigenvalue problems
    • V. Simoncini and M. Sadkane, Arnoldi-Riccati method for large eigenvalue problems, BIT, 36 (1996), pp. 578-593.
    • (1996) BIT , vol.36 , pp. 578-593
    • Simoncini, V.1    Sadkane, M.2
  • 23
    • 0009139884 scopus 로고
    • Matrix calculation for Liapunov quadratic forms
    • R. A. Smith, Matrix calculation for Liapunov quadratic forms, J. Differential Equations, 2 (1966), pp. 208-217.
    • (1966) J. Differential Equations , vol.2 , pp. 208-217
    • Smith, R.A.1
  • 25
    • 0000058177 scopus 로고
    • On the separation of two matrices
    • J. M. Varah, On the separation of two matrices. Linear Algebra Appl., (1979), pp. 216-222.
    • (1979) Linear Algebra Appl. , pp. 216-222
    • Varah, J.M.1
  • 26
    • 1542693348 scopus 로고
    • Linear matrix equations, controllability and observability, and the rank of solutions
    • H. K. Wimmer, Linear matrix equations, controllability and observability, and the rank of solutions, SIAM J. Matrix Anal., 8 (1988), pp. 570-578.
    • (1988) SIAM J. Matrix Anal. , vol.8 , pp. 570-578
    • Wimmer, H.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.