메뉴 건너뛰기




Volumn 22, Issue 12, 2009, Pages 1786-1788

A lower bound for the product of eigenvalues of solutions to matrix equations

Author keywords

Eigenvalue; Matrix equation; Positive definite matrix; Symmetric matrix

Indexed keywords

EIGENVALUE; EIGENVALUES; LINEAR MATRIX EQUATIONS; LOWER BOUNDS; MATRIX EQUATION; MATRIX EQUATIONS; POSITIVE DEFINITE MATRIX; SYMMETRIC MATRIX; SYSTEMS AND CONTROL;

EID: 70349629548     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2009.06.020     Document Type: Article
Times cited : (20)

References (23)
  • 2
    • 67649881615 scopus 로고    scopus 로고
    • On the reflexive solutions of the matrix equation A X B + C Y D = E
    • Dehghan M., and Hajarian M. On the reflexive solutions of the matrix equation A X B + C Y D = E. Bull. Korean Math. Soc. 46 (2009) 511-519
    • (2009) Bull. Korean Math. Soc. , vol.46 , pp. 511-519
    • Dehghan, M.1    Hajarian, M.2
  • 3
    • 18444409047 scopus 로고    scopus 로고
    • Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
    • Wang Q.W. Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations. Comput. Math. Appl. 49 (2005) 641-650
    • (2005) Comput. Math. Appl. , vol.49 , pp. 641-650
    • Wang, Q.W.1
  • 4
    • 18444385093 scopus 로고    scopus 로고
    • The general solution to a system of real quaternion matrix equations
    • Wang Q.W. The general solution to a system of real quaternion matrix equations. Comput. Math. Appl. 49 (2005) 665-675
    • (2005) Comput. Math. Appl. , vol.49 , pp. 665-675
    • Wang, Q.W.1
  • 5
    • 40849138243 scopus 로고    scopus 로고
    • The reflexive re-nonnegative definite solution to a quaternion matrix equation
    • Wang Q.W., and Zhang F. The reflexive re-nonnegative definite solution to a quaternion matrix equation. Electron. J. Linear Algebra 17 (2008) 88-101
    • (2008) Electron. J. Linear Algebra , vol.17 , pp. 88-101
    • Wang, Q.W.1    Zhang, F.2
  • 6
    • 58149346165 scopus 로고    scopus 로고
    • Weighted least squares solutions to general coupled Sylvester matrix equations
    • Zhou B., Li Z.Y., Duan G.R., and Wang Y. Weighted least squares solutions to general coupled Sylvester matrix equations. J. Comput. Appl. Math. 224 (2009) 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
  • 7
    • 67349285076 scopus 로고    scopus 로고
    • On Smith-type iterative algorithms for the Stein matrix equation
    • Zhou B., Lam J., and Duan G.R. On Smith-type iterative algorithms for the Stein matrix equation. Appl. Math. Lett. 22 (2009) 1038-1044
    • (2009) Appl. Math. Lett. , vol.22 , pp. 1038-1044
    • Zhou, B.1    Lam, J.2    Duan, G.R.3
  • 8
    • 26244448321 scopus 로고    scopus 로고
    • Gradient based iterative algorithms for solving a class of matrix equations
    • Ding F., and Chen T. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans. Automat. Control 50 (2005) 1216-1221
    • (2005) IEEE Trans. Automat. Control , vol.50 , pp. 1216-1221
    • Ding, F.1    Chen, T.2
  • 9
    • 22144434326 scopus 로고    scopus 로고
    • Hierarchical gradient-based identification of multivariable discrete-time systems
    • Ding F., and Chen T. Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41 (2005) 315-325
    • (2005) Automatica , vol.41 , pp. 315-325
    • Ding, F.1    Chen, T.2
  • 10
    • 10444247504 scopus 로고    scopus 로고
    • Iterative least squares solutions of coupled Sylvester matrix equations
    • Ding F., and Chen T. Iterative least squares solutions of coupled Sylvester matrix equations. Systems Control Lett. 54 (2005) 95-107
    • (2005) Systems Control Lett. , vol.54 , pp. 95-107
    • Ding, F.1    Chen, T.2
  • 11
    • 16244397443 scopus 로고    scopus 로고
    • Hierarchical least squares identification methods for multivariable systems
    • Ding F., and Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Automat. Control 50 (2005) 397-402
    • (2005) IEEE Trans. Automat. Control , vol.50 , pp. 397-402
    • Ding, F.1    Chen, T.2
  • 12
    • 33751185751 scopus 로고    scopus 로고
    • On iterative solutions of general coupled matrix equations
    • Ding F., and Chen T. On iterative solutions of general coupled matrix equations. SIAM J. Control Optim. 44 (2006) 2269-2284
    • (2006) SIAM J. Control Optim. , vol.44 , pp. 2269-2284
    • Ding, F.1    Chen, T.2
  • 13
    • 30844444393 scopus 로고    scopus 로고
    • A new solution to the generalized Sylvester matrix equation A V - E V F = B W
    • Zhou B., and Duan G.R. A new solution to the generalized Sylvester matrix equation A V - E V F = B W. Systems Control Lett. 55 (2006) 193-198
    • (2006) Systems Control Lett. , vol.55 , pp. 193-198
    • Zhou, B.1    Duan, G.R.2
  • 14
    • 34249092654 scopus 로고    scopus 로고
    • Solutions to generalized Sylvester matrix equation by Schur decomposition
    • Zhou B., and Duan G.R. Solutions to generalized Sylvester matrix equation by Schur decomposition. Internat. J. Systems Sci. 38 (2007) 369-375
    • (2007) Internat. J. Systems Sci. , vol.38 , pp. 369-375
    • Zhou, B.1    Duan, G.R.2
  • 15
    • 43049136924 scopus 로고    scopus 로고
    • On the generalized Sylvester mapping and matrix equations
    • Zhou B., and Duan G.R. On the generalized Sylvester mapping and matrix equations. Systems Control Lett. 57 (2008) 200-208
    • (2008) Systems Control Lett. , vol.57 , pp. 200-208
    • Zhou, B.1    Duan, G.R.2
  • 16
    • 55849110814 scopus 로고    scopus 로고
    • An iterative algorithm for solving a pair of matrix equations A Y B = E, C Y D = F over generalized centro-symmetric matrices
    • Dehghan M., and Hajarian M. An iterative algorithm for solving a pair of matrix equations A Y B = E, C Y D = F over generalized centro-symmetric matrices. Comput. Math. Appl. 56 (2008) 3246-3260
    • (2008) Comput. Math. Appl. , vol.56 , pp. 3246-3260
    • Dehghan, M.1    Hajarian, M.2
  • 17
    • 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., and Hajarian M. An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation. Appl. Math. Comput. 202 (2008) 571-588
    • (2008) Appl. Math. Comput. , vol.202 , pp. 571-588
    • Dehghan, M.1    Hajarian, M.2
  • 19
    • 0022147869 scopus 로고
    • On bounds of the Riccati and Lyapunov matrix equations
    • Kwon B.H., Youn M.J., and Bien Z. On bounds of the Riccati and Lyapunov matrix equations. IEEE Trans. Automat. Control Ac-30 (1985) 1134-1135
    • (1985) IEEE Trans. Automat. Control , vol.Ac-30 , pp. 1134-1135
    • Kwon, B.H.1    Youn, M.J.2    Bien, Z.3
  • 20
    • 0023855628 scopus 로고
    • Simultaneous eigenvalue lower bounds for the Lyapunov matrix equation
    • Komaroff N. Simultaneous eigenvalue lower bounds for the Lyapunov matrix equation. IEEE Trans. Automat. Control 33 (1988) 126-128
    • (1988) IEEE Trans. Automat. Control , vol.33 , pp. 126-128
    • Komaroff, N.1
  • 22
    • 0024612165 scopus 로고
    • Simultaneous eigenvalue lower bounds for the Riccati matrix equation
    • Komaroff N. Simultaneous eigenvalue lower bounds for the Riccati matrix equation. IEEE Trans. Automat. Control 34 (1989) 175-177
    • (1989) IEEE Trans. Automat. Control , vol.34 , pp. 175-177
    • Komaroff, N.1
  • 23
    • 84918290550 scopus 로고
    • Bibliography on bounds for characteristic roots of finite matrices
    • Taussky O. Bibliography on bounds for characteristic roots of finite matrices. National Bureau of Standards (September,1951)
    • (1951) National Bureau of Standards
    • Taussky, O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.