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Volumn 28, Issue 4, 2006, Pages 1029-1051

Structured polynomial eigenvalue problems: Good vibrations from good linearizations

Author keywords

Cayley transformation; Even matrix polynomial; Nonlinear eigenvalue problem; Odd matrix polynomial; Palindromic matrix polynomial; Preservation of eigenvalue symmetry; Structured linearization

Indexed keywords

CAYLEY TRANSFORMATION; EVEN MATRIX POLYNOMIAL; NONLINEAR EIGENVALUE PROBLEM; ODD MATRIX POLYNOMIAL; PALINDROMIC; PALINDROMIC MATRIX POLYNOMIAL; PRESERVATION OF EIGENVALUE SYMMETRY; STRUCTURED LINEARIZATION;

EID: 33947378022     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050628362     Document Type: Conference Paper
Times cited : (259)

References (36)
  • 3
    • 0037200577 scopus 로고    scopus 로고
    • Structured eigenvalue methods for the computation of corner singularities in 3D anisotropic elastic structures
    • T. APEL, V. MEHRMANN, AND D. WATKINS, Structured eigenvalue methods for the computation of corner singularities in 3D anisotropic elastic structures., Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 4459-4473.
    • (2002) Comput. Methods Appl. Mech. Engrg , vol.191 , pp. 4459-4473
    • APEL, T.1    MEHRMANN, V.2    WATKINS, D.3
  • 4
    • 35348959807 scopus 로고    scopus 로고
    • T. APEL, V. MEHRMANN, AND D. WATKINS, Numerical solution of large scale structured polynomial or rational eigenvalue problems, in Foundations of Computational Mathematics, (Minneapolis 2002), F. Cucker and P. Olver, eds., London Math. Soc. Lecture Note Ser. 312, Cambridge University Press, Cambridge, UK, 2004, pp. 137-157.
    • T. APEL, V. MEHRMANN, AND D. WATKINS, Numerical solution of large scale structured polynomial or rational eigenvalue problems, in Foundations of Computational Mathematics, (Minneapolis 2002), F. Cucker and P. Olver, eds., London Math. Soc. Lecture Note Ser. 312, Cambridge University Press, Cambridge, UK, 2004, pp. 137-157.
  • 5
    • 0037289010 scopus 로고    scopus 로고
    • Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils
    • P. BENNER, R. BYERS, V. MEHRMANN, AND H. XU, Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 165-190.
    • (2002) SIAM J. Matrix Anal. Appl , vol.24 , pp. 165-190
    • BENNER, P.1    BYERS, R.2    MEHRMANN, V.3    XU, H.4
  • 9
    • 2542426818 scopus 로고    scopus 로고
    • General isospectral flows for linear dynamic systems
    • S. GARVEY, U. PRELLS, M. FRISWELL, AND Z. CHEN, General isospectral flows for linear dynamic systems, Linear Algebra Appl., 385 (2004), pp. 335-368.
    • (2004) Linear Algebra Appl , vol.385 , pp. 335-368
    • GARVEY, S.1    PRELLS, U.2    FRISWELL, M.3    CHEN, Z.4
  • 10
    • 0002609440 scopus 로고
    • General theory of regular matrix polynomials and band Toeplitz operators
    • I. GOHBERG, M. A. KAASHOEK, AND P. LANCASTER, General theory of regular matrix polynomials and band Toeplitz operators, Integral Equations Operator Theory, 11 (1988), pp. 776-882.
    • (1988) Integral Equations Operator Theory , vol.11 , pp. 776-882
    • GOHBERG, I.1    KAASHOEK, M.A.2    LANCASTER, P.3
  • 14
    • 34547394717 scopus 로고    scopus 로고
    • The conditioning of linearizations of matrix polynomials
    • N. J. HIGHAM, D. S. MACKEY, AND F. TISSEUR, The conditioning of linearizations of matrix polynomials, SIAM J. Matrix Anal. Appl., 28 (2006), 1005-1028.
    • (2006) SIAM J. Matrix Anal. Appl , vol.28 , pp. 1005-1028
    • HIGHAM, N.J.1    MACKEY, D.S.2    TISSEUR, F.3
  • 15
    • 31244435530 scopus 로고    scopus 로고
    • Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems
    • N. J. HIGHAM, F. TISSEUR, AND P. M. V. DOOREN, Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems, Linear Algebra Appl., 351/352 (2002), pp. 455-474.
    • (2002) Linear Algebra Appl , vol.351-352 , pp. 455-474
    • HIGHAM, N.J.1    TISSEUR, F.2    DOOREN, P.M.V.3
  • 18
    • 35349005056 scopus 로고    scopus 로고
    • Personal communication
    • P. HILTON, Personal communication, 2004.
    • (2004)
    • HILTON, P.1
  • 19
    • 35349021343 scopus 로고    scopus 로고
    • Inventing a palindrome
    • P. HILTON, Inventing a palindrome, College Math. J., 5 (1999), p. 422.
    • (1999) College Math. J , vol.5 , pp. 422
    • HILTON, P.1
  • 20
    • 31544482216 scopus 로고    scopus 로고
    • Accurate eigenvalues for fast trains
    • 9, Nov
    • I. C. F. IPSEN, Accurate eigenvalues for fast trains, SIAM News, 37(9), Nov. 2004, pp. 1-2.
    • (2004) SIAM News
    • IPSEN, I.C.F.1
  • 23
    • 54849407894 scopus 로고    scopus 로고
    • A Note on Weak and Strong Linearizations of Regular Matrix Polynomials
    • Manchester Centre for Computational Mathematics, Manchester, UK
    • P. LANCASTER AND P. PSARRAKOS, A Note on Weak and Strong Linearizations of Regular Matrix Polynomials, Numerical Analysis Report 470, Manchester Centre for Computational Mathematics, Manchester, UK, 2005.
    • (2005) Numerical Analysis Report , vol.470
    • LANCASTER, P.1    PSARRAKOS, P.2
  • 25
    • 0000128421 scopus 로고
    • Computation of 3d-singularities in elasticity, in Boundary Value Problems and Integral Equations in Nonsmooth Domains
    • M. Costabel, M. Dauge, and S. Nicaise, eds, Marcel Dekker, New York
    • D. LEGUILLON, Computation of 3d-singularities in elasticity, in Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge, and S. Nicaise, eds., Lecture Notes in Pure Appl. Math. 167, Marcel Dekker, New York, 1995, pp. 161-170.
    • (1995) Lecture Notes in Pure Appl. Math , vol.167 , pp. 161-170
    • LEGUILLON, D.1
  • 29
    • 33746041687 scopus 로고    scopus 로고
    • Structured factorizations in scalar product spaces
    • D. S. MACKEY, N. MACKEY, AND F. TISSEUR, Structured factorizations in scalar product spaces, SIAM J. Matrix Anal. Appl., 27 (2006), pp. 821-850.
    • (2006) SIAM J. Matrix Anal. Appl , vol.27 , pp. 821-850
    • MACKEY, D.S.1    MACKEY, N.2    TISSEUR, F.3
  • 30
    • 35349029613 scopus 로고    scopus 로고
    • 5. The MathWorks, Inc, Natick, MA
    • MATLAB, Version 5. The MathWorks, Inc., Natick, MA, 1996.
    • (1996) MATLAB, Version
  • 31
    • 0002467383 scopus 로고
    • The Autonomous Linear Quadratic Control Problem, Theory and Numerical Solution
    • Springer-Verlag, Heidelberg
    • V. MEHRMANN, The Autonomous Linear Quadratic Control Problem, Theory and Numerical Solution, Lecture Notes in Control and Inform. Sci. 163, Springer-Verlag, Heidelberg, 1991.
    • (1991) Lecture Notes in Control and Inform. Sci , vol.163
    • MEHRMANN, V.1
  • 32
    • 21344456693 scopus 로고    scopus 로고
    • A step toward a unified treatment of continuous and discrete time control problems
    • V. MEHRMANN, A step toward a unified treatment of continuous and discrete time control problems, Linear Algebra Appl., 241/243 (1996), pp. 749-779.
    • (1996) Linear Algebra Appl , vol.241-243 , pp. 749-779
    • MEHRMANN, V.1
  • 33
    • 0035679127 scopus 로고    scopus 로고
    • Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils
    • V. MEHRMANN AND D. WATKINS, Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils, SIAM J. Sci. Comput., 22 (2001), pp. 1905-1925.
    • (2001) SIAM J. Sci. Comput , vol.22 , pp. 1905-1925
    • MEHRMANN, V.1    WATKINS, D.2
  • 34
    • 0041515149 scopus 로고    scopus 로고
    • Polynomial eigenvalue problems with Hamiltonian structure
    • V. MEHRMANN AND D. WATKINS, Polynomial eigenvalue problems with Hamiltonian structure, Electron. Trans. Numer. Anal., 13 (2002), pp. 106-118.
    • (2002) Electron. Trans. Numer. Anal , vol.13 , pp. 106-118
    • MEHRMANN, V.1    WATKINS, D.2
  • 35
    • 0035359418 scopus 로고    scopus 로고
    • The quadratic eigenvalue problem
    • F. TISSEUR AND K. MEERBERGEN, The quadratic eigenvalue problem, SIAM Rev., 43 (2001), pp. 235-286.
    • (2001) SIAM Rev , vol.43 , pp. 235-286
    • TISSEUR, F.1    MEERBERGEN, K.2
  • 36
    • 35348953563 scopus 로고    scopus 로고
    • Diplomarbeit, Institute of Computational Mathematics, Johannes Kepler University Linz, Linz, Austria
    • S. ZAGLMAYR, Eigenvalue Problems in SAW-Filter Simulations, Diplomarbeit, Institute of Computational Mathematics, Johannes Kepler University Linz, Linz, Austria, 2002.
    • (2002) Eigenvalue Problems in SAW-Filter Simulations
    • ZAGLMAYR, S.1


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