메뉴 건너뛰기




Volumn 358, Issue 1-3, 2003, Pages 5-22

Bounds for eigenvalues of matrix polynomials

Author keywords

Matrix; Block companion matrix; Gershgorin's theorem; Matrix polynomial; Numerical radius; Polynomial eigenvalue problem

Indexed keywords


EID: 84867975401     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00316-0     Document Type: Conference Paper
Times cited : (95)

References (25)
  • 2
    • 0030571227 scopus 로고    scopus 로고
    • Some large-scale matrix computation problems
    • Z. Bai, M. Fahey, and G.H. Golub Some large-scale matrix computation problems J. Comput. Appl. Math. 74 1996 71 89
    • (1996) J. Comput. Appl. Math. , vol.74 , pp. 71-89
    • Bai, Z.1    Fahey, M.2    Golub, G.H.3
  • 3
    • 0009924116 scopus 로고    scopus 로고
    • Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices
    • Z. Bai, and G.H. Golub Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices Ann. Number. Math. 4 1997 29 38
    • (1997) Ann. Number. Math. , vol.4 , pp. 29-38
    • Bai, Z.1    Golub, G.H.2
  • 4
    • 0034503570 scopus 로고    scopus 로고
    • Iterative system solvers for the frequency analysis of linear mechanical systems
    • A. Feriani, F. Perotti, and V. Simoncini Iterative system solvers for the frequency analysis of linear mechanical systems Comput. Methods Appl. Mech. Eng. 19 13-14 2000 1719 1739
    • (2000) Comput. Methods Appl. Mech. Eng. , vol.19 , Issue.1314 , pp. 1719-1739
    • Feriani, A.1    Perotti, F.2    Simoncini, V.3
  • 5
    • 84968495078 scopus 로고
    • Buzano's inequality and bounds for roots of algebraic equations
    • M. Fujii, and F. Kubo Buzano's inequality and bounds for roots of algebraic equations Proc. Amer. Math. Soc. 117 2 1993 359 361
    • (1993) Proc. Amer. Math. Soc. , vol.117 , Issue.2 , pp. 359-361
    • Fujii, M.1    Kubo, F.2
  • 7
    • 0034144755 scopus 로고    scopus 로고
    • A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra
    • N.J. Higham, and F. Tisseur A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra SIAM J. Matrix Anal. Appl. 21 4 2000 1185 1201
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , Issue.4 , pp. 1185-1201
    • Higham, N.J.1    Tisseur, F.2
  • 8
    • 10044261283 scopus 로고    scopus 로고
    • More on pseudospectra for polynomial eigenvalue problems and applications in control theory
    • Manchester Centre for Computational Mathematics, Manchester, UK, January 2001
    • N.J. Higham, F. Tisseur, More on pseudospectra for polynomial eigenvalue problems and applications in control theory, Numerical Analysis Report 372, Manchester Centre for Computational Mathematics, Manchester, UK, January 2001
    • Numerical Analysis Report 372
    • Higham, N.J.1    Tisseur, F.2
  • 9
    • 0004151494 scopus 로고
    • Cambridge University Press ISBN 0-521-30586-1
    • R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, 1985, xiii+561 pp., ISBN 0-521-30586-1
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 11
    • 0024144969 scopus 로고
    • Controllability and stability radii for companion form systems
    • C. Kenney, and A.J. Laub Controllability and stability radii for companion form systems Math. Control Signals Systems 1 1988 239 256
    • (1988) Math. Control Signals Systems , vol.1 , pp. 239-256
    • Kenney, C.1    Laub, A.J.2
  • 12
    • 21844515195 scopus 로고
    • Singular values of companion matrices and bounds on zeros of polynomials
    • F. Kittaneh Singular values of companion matrices and bounds on zeros of polynomials SIAM J. Matrix Anal. Appl. 16 1 1995 333 340
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , Issue.1 , pp. 333-340
    • Kittaneh, F.1
  • 14
    • 0000017859 scopus 로고
    • Quadratic eigenvalue problems
    • P. Lancaster Quadratic eigenvalue problems Linear Algebra Appl. 150 1991 499 506
    • (1991) Linear Algebra Appl. , vol.150 , pp. 499-506
    • Lancaster, P.1
  • 16
    • 0004015440 scopus 로고    scopus 로고
    • Prindle, Weber and Schmidt, Boston, 1964. Reprinted by Dover, New York, 1992, ISBN 0-486-67102-X
    • M. Marcus, H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Prindle, Weber and Schmidt, Boston, 1964. Reprinted by Dover, New York, 1992, ISBN 0-486-67102-X
    • A Survey of Matrix Theory and Matrix Inequalities
    • Marcus, M.1    Minc, H.2
  • 17
    • 0003363945 scopus 로고
    • Geometry of Polynomials
    • second ed., AMS, Providence, RI, USA
    • M. Marden, Geometry of Polynomials, Mathematical Surveys, vol. 3, second ed., AMS, Providence, RI, USA, 1966, xiii+243 pp
    • (1966) Mathematical Surveys , vol.3
    • Marden, M.1
  • 18
    • 0039686475 scopus 로고
    • On the zeros of polynomials
    • Q.G. Mohammad On the zeros of polynomials Amer. Math. Monthly 72 1 1965 35 38
    • (1965) Amer. Math. Monthly , vol.72 , Issue.1 , pp. 35-38
    • Mohammad, Q.G.1
  • 19
    • 0039686475 scopus 로고
    • On the zeros of polynomials
    • Q.G. Mohammad On the zeros of polynomials Amer. Math. Monthly 72 6 1965 631 633
    • (1965) Amer. Math. Monthly , vol.72 , Issue.6 , pp. 631-633
    • Mohammad, Q.G.1
  • 22
    • 84867987858 scopus 로고    scopus 로고
    • 2A+λB+C)x=b and appication to structural dynamics
    • Istituto di Analisi Numerica del CNR, Pavia, Italy, December 2000
    • 2A+λB+C)x=b and appication to structural dynamics, Technical Report 1197, Istituto di Analisi Numerica del CNR, Pavia, Italy, December 2000
    • Technical Report 1197
    • Simoncini, V.1    Perotti, F.2
  • 23
    • 84867995569 scopus 로고    scopus 로고
    • Strucutred pseudospectra for polynomial eigenvalue problems with applications
    • Manchester Centre for Computational Mathematics, Manchester, UK, April 2000. To appear in SIAM J. Matrix Anal. Appl
    • F. Tisseur, N.J. Higham, Strucutred pseudospectra for polynomial eigenvalue problems with applications, Numerical Analysis Report No. 359, Manchester Centre for Computational Mathematics, Manchester, UK, April 2000. To appear in SIAM J. Matrix Anal. Appl
    • Numerical Analysis Report No. 359
    • Tisseur, F.1    Higham, N.J.2
  • 24
    • 0035359418 scopus 로고    scopus 로고
    • The quadratic eigenvalue problem
    • F. Tisseur, and K. Meerbergen The quadratic eigenvalue problem SIAM Rev. 43 2 2001
    • (2001) SIAM Rev. , vol.43 , Issue.2
    • Tisseur, F.1    Meerbergen, K.2
  • 25
    • 0003942612 scopus 로고
    • Addison-Wesley, Reading, MA, USA x+492+appendices pp. Reprinted by Dover, New York, 1988, ISBN 0-486-65691-8
    • D.M. Young, R.T. Gregory, A survey of Numerical Mathematics, vol. 1, Addison-Wesley, Reading, MA, USA, 1972. x+492+appendices pp. Reprinted by Dover, New York, 1988, ISBN 0-486-65691-8
    • (1972) A Survey of Numerical Mathematics , vol.1
    • Young, D.M.1    Gregory, R.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.