메뉴 건너뛰기




Volumn 35, Issue 3, 2011, Pages 1065-1080

Finite iterative solutions to coupled Sylvester-conjugate matrix equations

Author keywords

Coupled Sylvester conjugate matrix equation; Finite iterative solution; Inner product; Orthogonality

Indexed keywords

CANONICAL FORM; COEFFICIENT MATRIX; COMPLEX MATRICES; GENERALIZED SYLVESTER MATRIX EQUATION; INITIAL VALUES; INNER PRODUCT; ITERATION STEP; ITERATIVE ALGORITHM; ITERATIVE SOLUTIONS; KIND OF MATRIXES; LYAPUNOV MATRIX EQUATIONS; MATRIX EQUATIONS; NUMERICAL EXAMPLE; ORTHOGONALITY; ROUND-OFF ERRORS;

EID: 78549235743     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.07.053     Document Type: Article
Times cited : (63)

References (41)
  • 2
    • 0029375701 scopus 로고
    • Parallel computation of the solutions of coupled algebraic Lyapunov equations
    • Borno I. Parallel computation of the solutions of coupled algebraic Lyapunov equations. Automatica 1995, 31(9):1345-1347.
    • (1995) Automatica , vol.31 , Issue.9 , pp. 1345-1347
    • Borno, I.1
  • 3
    • 0039428375 scopus 로고
    • A direct method for reordering eigenvalues in the generalized real Schur form of a regular matrix pair (A,B)
    • Kluwer Academic Publishers, Amsterdam, M.S. Moonen, G.H. Golub, B.L.R. De Moor (Eds.)
    • Kagstrom B. A direct method for reordering eigenvalues in the generalized real Schur form of a regular matrix pair (A,B). Linear Algebra for Large Scale and Real-time Application 1993, 195-218. Kluwer Academic Publishers, Amsterdam. M.S. Moonen, G.H. Golub, B.L.R. De Moor (Eds.).
    • (1993) Linear Algebra for Large Scale and Real-time Application , pp. 195-218
    • Kagstrom, B.1
  • 4
    • 0040740214 scopus 로고
    • A generalized state-space approach for the additive decomposition of a transfer matrix
    • Kagstrom B., Van Dooren P. A generalized state-space approach for the additive decomposition of a transfer matrix. Int. J. Numer. Linear Algebra Appl. 1992, 1(2):165-181.
    • (1992) Int. J. Numer. Linear Algebra Appl. , vol.1 , Issue.2 , pp. 165-181
    • Kagstrom, B.1    Van Dooren, P.2
  • 5
    • 0024700168 scopus 로고
    • Generalized Schur methods with condition estimators for solving the generalized Sylvester equation
    • Kagstrom B., Westin L. Generalized Schur methods with condition estimators for solving the generalized Sylvester equation. IEEE Trans. Autom. Control 1989, 34(7):745-751.
    • (1989) IEEE Trans. Autom. Control , vol.34 , Issue.7 , pp. 745-751
    • Kagstrom, B.1    Westin, L.2
  • 6
    • 33845392294 scopus 로고
    • Stability results for discrete-time linear systems with Markovian jumping parameters
    • Costa O.L.V., Fragoso M.D. Stability results for discrete-time linear systems with Markovian jumping parameters. J. Math. Anal. Appl. 1993, 179(1):154-178.
    • (1993) J. Math. Anal. Appl. , vol.179 , Issue.1 , pp. 154-178
    • Costa, O.L.V.1    Fragoso, M.D.2
  • 7
    • 27344436251 scopus 로고    scopus 로고
    • The optimal solution of linear matrix equation by matrix decompositions
    • Yuan Y.X. The optimal solution of linear matrix equation by matrix decompositions. Math. Numer. Sin. 2002, 24:165-176.
    • (2002) Math. Numer. Sin. , vol.24 , pp. 165-176
    • Yuan, Y.X.1
  • 8
    • 27344432689 scopus 로고    scopus 로고
    • Least-squares solution with the minimum-norm for the matrix equation (AXB,GXH)=(C,D)
    • Liao A.P., Lei Y. Least-squares solution with the minimum-norm for the matrix equation (AXB,GXH)=(C,D). Comput. Math. Appl. 2005, 50:539-549.
    • (2005) Comput. Math. Appl. , vol.50 , pp. 539-549
    • Liao, A.P.1    Lei, Y.2
  • 9
    • 58549084763 scopus 로고    scopus 로고
    • The *congruence class of the solutions of some matrix equations
    • Zheng B., Ye L., Cvetkoic-Illic D.S. The *congruence class of the solutions of some matrix equations. Comput. Math. Appl. 2009, 57:540-549.
    • (2009) Comput. Math. Appl. , vol.57 , pp. 540-549
    • Zheng, B.1    Ye, L.2    Cvetkoic-Illic, D.S.3
  • 10
    • 0029393130 scopus 로고
    • Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems
    • Borno I., Gajic Z. Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems. Comput. Math. Appl. 1995, 30(7):1-4.
    • (1995) Comput. Math. Appl. , vol.30 , Issue.7 , pp. 1-4
    • Borno, I.1    Gajic, Z.2
  • 11
    • 37649024692 scopus 로고    scopus 로고
    • Iterative solutions of coupled discrete Markovian jump Lyapunov equations
    • Wang Q., Lam J., Wei Y., Chen T. Iterative solutions of coupled discrete Markovian jump Lyapunov equations. Comput. Math. Appl. 2008, 55(4):843-850.
    • (2008) Comput. Math. Appl. , vol.55 , Issue.4 , pp. 843-850
    • Wang, Q.1    Lam, J.2    Wei, Y.3    Chen, T.4
  • 12
    • 78549238953 scopus 로고    scopus 로고
    • A finite iterative algorithm for solving coupled Lyapunov equations appearing in discrete-time Markov jump linear systems, IET Control Theory Appl., in press.
    • L. Tong, A.G. Wu, G.R. Duan, A finite iterative algorithm for solving coupled Lyapunov equations appearing in discrete-time Markov jump linear systems, IET Control Theory Appl., in press.
    • Tong, L.1    Wu, A.G.2    Duan, G.R.3
  • 13
    • 10444247504 scopus 로고    scopus 로고
    • Iterative least-squares solutions of coupled Sylvester matrix equations
    • Ding F., Chen T. Iterative least-squares solutions of coupled Sylvester matrix equations. Syst. Control Lett. 2005, 54:95-107.
    • (2005) Syst. Control Lett. , vol.54 , pp. 95-107
    • Ding, F.1    Chen, T.2
  • 14
    • 38949156204 scopus 로고    scopus 로고
    • Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
    • Ding F., Liu P.X., Ding J. Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Appl. Math. Comput. 2008, 197:41-50.
    • (2008) Appl. Math. Comput. , vol.197 , pp. 41-50
    • Ding, F.1    Liu, P.X.2    Ding, J.3
  • 15
    • 26244448321 scopus 로고    scopus 로고
    • Gradient based iterative algorithms for solving a class of matrix equations
    • Ding F., Chen T. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans. Autom. Control 2005, 50(8):1216-1221.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.8 , pp. 1216-1221
    • Ding, F.1    Chen, T.2
  • 16
    • 34249784200 scopus 로고    scopus 로고
    • Vector least-squares solutions for coupled singular matrix equations
    • Kilicman A., Zhour Z.A. Vector least-squares solutions for coupled singular matrix equations. J. Comput. Appl. Math. 2007, 206:1051-1069.
    • (2007) J. Comput. Appl. Math. , vol.206 , pp. 1051-1069
    • Kilicman, A.1    Zhour, Z.A.2
  • 17
    • 55649083103 scopus 로고    scopus 로고
    • Convergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations
    • Zhou B., Lam J., Duan G.R. Convergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations. Comput. Math. Appl. 2008, 56:3070-3078.
    • (2008) Comput. Math. Appl. , vol.56 , pp. 3070-3078
    • Zhou, B.1    Lam, J.2    Duan, G.R.3
  • 19
    • 55849110814 scopus 로고    scopus 로고
    • An iterative algorithm for solving a pair of matrix equations AYB=E, CYD=F over generalized centro-symmetric matrices
    • Dehghan M., Hajarian M. An iterative algorithm for solving a pair of matrix equations AYB=E, CYD=F over generalized centro-symmetric matrices. Comput. Math. Appl. 2008, 56:3246-3260.
    • (2008) Comput. Math. Appl. , vol.56 , pp. 3246-3260
    • Dehghan, M.1    Hajarian, M.2
  • 20
    • 48149092968 scopus 로고    scopus 로고
    • An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
    • Dehghan M., Hajarian M. An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation. Appl. Math. Comput. 2008, 202:571-588.
    • (2008) Appl. Math. Comput. , vol.202 , pp. 571-588
    • Dehghan, M.1    Hajarian, M.2
  • 21
    • 70350622178 scopus 로고    scopus 로고
    • An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices, Appl. Math. Model. doi:10.1016/j.apm.2009.06.018
    • M. Dehghan, M. Hajarian, An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices, Appl. Math. Model., doi:10.1016/j.apm.2009.06.018.
    • Dehghan, M.1    Hajarian, M.2
  • 22
    • 61449108996 scopus 로고    scopus 로고
    • Gradient based iterative algorithm for solving coupled matrix equations
    • Zhou B., Duan G.R., Li Z.Y. Gradient based iterative algorithm for solving coupled matrix equations. Syst. Control Lett. 2009, 58:327-333.
    • (2009) Syst. Control Lett. , vol.58 , pp. 327-333
    • Zhou, B.1    Duan, G.R.2    Li, Z.Y.3
  • 23
    • 58149346165 scopus 로고    scopus 로고
    • Weighted least squares solutions to general coupled Sylvester matrix equations
    • Zhou B., Li Z.Y., Duan G.R., Wang Y. Weighted least squares solutions to general coupled Sylvester matrix equations. J. Comput. Appl. Math. 2009, 224:759-776.
    • (2009) J. Comput. Appl. Math. , vol.224 , pp. 759-776
    • Zhou, B.1    Li, Z.Y.2    Duan, G.R.3    Wang, Y.4
  • 24
    • 34249107290 scopus 로고    scopus 로고
    • Kronecker maps and Sylvester-polynomial matrix equations
    • Wu A.G., Duan G.R., Xue Y. Kronecker maps and Sylvester-polynomial matrix equations. IEEE Trans. Autom. Control 2007, 52(5):905-910.
    • (2007) IEEE Trans. Autom. Control , vol.52 , Issue.5 , pp. 905-910
    • Wu, A.G.1    Duan, G.R.2    Xue, Y.3
  • 25
    • 42649141973 scopus 로고    scopus 로고
    • Solution to generalized Sylvester matrix equations
    • Wu A.G., Duan G.R., Zhou B. Solution to generalized Sylvester matrix equations. IEEE Trans. Autom. Control 2008, 53(3):811-815.
    • (2008) IEEE Trans. Autom. Control , vol.53 , Issue.3 , pp. 811-815
    • Wu, A.G.1    Duan, G.R.2    Zhou, B.3
  • 26
    • 78549271762 scopus 로고    scopus 로고
    • A closed-form solution to the nonhomogeneous generalized Sylvester matrix equation, IET Control Theory Appl., in press.
    • A.G. Wu, Y. Sun, G. Feng, A closed-form solution to the nonhomogeneous generalized Sylvester matrix equation, IET Control Theory Appl., in press.
    • Wu, A.G.1    Sun, Y.2    Feng, G.3
  • 27
    • 34248552567 scopus 로고
    • Consimilarity and the matrix equation AX̄-XB=C
    • North-Holland, New York, (Auburn, Ala., 1986)
    • Bevis J.H., Hall F.J., Hartwing R.E. Consimilarity and the matrix equation AX̄-XB=C. Current Trends in Matrix Theory 1987, 51-64. North-Holland, New York, (Auburn, Ala., 1986).
    • (1987) Current Trends in Matrix Theory , pp. 51-64
    • Bevis, J.H.1    Hall, F.J.2    Hartwing, R.E.3
  • 29
    • 0035400240 scopus 로고    scopus 로고
    • Consimilarity of quaternion matrices and complex matrices
    • Huang L. Consimilarity of quaternion matrices and complex matrices. Linear Algebra Appl. 2001, 331:21-30.
    • (2001) Linear Algebra Appl. , vol.331 , pp. 21-30
    • Huang, L.1
  • 30
    • 33745812086 scopus 로고    scopus 로고
    • An algebraic relation between consimilarity and similarity of complex matrices and its applications
    • Jiang T., Cheng X., Chen L. An algebraic relation between consimilarity and similarity of complex matrices and its applications. J. Phys. A: Math. Gen. 2006, 39:9215-9222.
    • (2006) J. Phys. A: Math. Gen. , vol.39 , pp. 9215-9222
    • Jiang, T.1    Cheng, X.2    Chen, L.3
  • 32
    • 33845748742 scopus 로고    scopus 로고
    • On solutions of XF-AX=C and XF-AX̄=C
    • Wu A.G., Duan G.R., Yu H.H. On solutions of XF-AX=C and XF-AX̄=C. Appl. Math. Appl. 2006, 182(2):932-941.
    • (2006) Appl. Math. Appl. , vol.182 , Issue.2 , pp. 932-941
    • Wu, A.G.1    Duan, G.R.2    Yu, H.H.3
  • 33
    • 0037720091 scopus 로고    scopus 로고
    • On solutions of the matrix equations X-AXB=C and X-AX̄B=C
    • Jiang T., Wei M. On solutions of the matrix equations X-AXB=C and X-AX̄B=C. Linear Algebra Appl. 2003, 367:225-233.
    • (2003) Linear Algebra Appl. , vol.367 , pp. 225-233
    • Jiang, T.1    Wei, M.2
  • 34
    • 67349254484 scopus 로고    scopus 로고
    • On matrix equations X-AXF=C and X-AX̄F=C
    • Wu A.G., Wang H.Q., Duan G.R. On matrix equations X-AXF=C and X-AX̄F=C. J. Comput. Appl. Math. 2009, 230(2):690-698.
    • (2009) J. Comput. Appl. Math. , vol.230 , Issue.2 , pp. 690-698
    • Wu, A.G.1    Wang, H.Q.2    Duan, G.R.3
  • 35
    • 42749083362 scopus 로고    scopus 로고
    • On solutions of matrix equations V-AVF=BW and V-AV̄F=BW
    • Wu A.G., Fu Y.M., Duan G.R. On solutions of matrix equations V-AVF=BW and V-AV̄F=BW. Math. Comput. Model. 2008, 47(11-12):1181-1197.
    • (2008) Math. Comput. Model. , vol.47 , Issue.11-12 , pp. 1181-1197
    • Wu, A.G.1    Fu, Y.M.2    Duan, G.R.3
  • 36
    • 67649199012 scopus 로고    scopus 로고
    • Closed-form solutions to the nonhomogeneous Yakubovich-conjugate matrix equation
    • Wu A.G., Feng G., Hu J., Duan G.R. Closed-form solutions to the nonhomogeneous Yakubovich-conjugate matrix equation. Appl. Math. Comput. 2009, 214:442-450.
    • (2009) Appl. Math. Comput. , vol.214 , pp. 442-450
    • Wu, A.G.1    Feng, G.2    Hu, J.3    Duan, G.R.4
  • 37
    • 77953131907 scopus 로고    scopus 로고
    • Closed-form solutions to Sylvester-conjugate matrix equations
    • Wu A.G., Feng G., Duan G.R., Wu W.J. Closed-form solutions to Sylvester-conjugate matrix equations. Comput. Math. Appl. 2010, 60(1):95-111.
    • (2010) Comput. Math. Appl. , vol.60 , Issue.1 , pp. 95-111
    • Wu, A.G.1    Feng, G.2    Duan, G.R.3    Wu, W.J.4
  • 38
    • 77955425442 scopus 로고    scopus 로고
    • Iterative solutions to the extended Sylvester-conjugate matrix equation
    • Wu A.G., Zeng X., Duan G.R., Wu W.J. Iterative solutions to the extended Sylvester-conjugate matrix equation. Appl. Math. Comput. 2010, 217(1):130-142.
    • (2010) Appl. Math. Comput. , vol.217 , Issue.1 , pp. 130-142
    • Wu, A.G.1    Zeng, X.2    Duan, G.R.3    Wu, W.J.4
  • 39
    • 77956010192 scopus 로고    scopus 로고
    • Finite iterative solutions to a class of complex matrix equations with conjugate and transpose of the unknowns, Math. Comput. Model. doi:10.1016/j.mcm.2010.06.010
    • A.G. Wu, G. Feng, G.R. Duan, W.J. Wu, Finite iterative solutions to a class of complex matrix equations with conjugate and transpose of the unknowns, Math. Comput. Model. (2010), doi:10.1016/j.mcm.2010.06.010.
    • (2010)
    • Wu, A.G.1    Feng, G.2    Duan, G.R.3    Wu, W.J.4
  • 40
    • 77953135303 scopus 로고    scopus 로고
    • Iterative solutions to coupled Sylvester-conjugate matrix equations
    • Wu A.G., Feng G., Duan G.R., Wu W.J. Iterative solutions to coupled Sylvester-conjugate matrix equations. Comput. Math. Appl. 2010, 60(1):54-66.
    • (2010) Comput. Math. Appl. , vol.60 , Issue.1 , pp. 54-66
    • Wu, A.G.1    Feng, G.2    Duan, G.R.3    Wu, W.J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.