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Volumn 78, Issue 3, 1998, Pages 329-358

A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils

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EID: 0032344706     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050315     Document Type: Article
Times cited : (113)

References (29)
  • 1
    • 0003100242 scopus 로고
    • On Hamiltonian and symplectic Hessenberg forms
    • Ammar, G.S., Mehrmann, V. (1991): On Hamiltonian and symplectic Hessenberg forms. Linear Algebra Appl. 149, 55-72
    • (1991) Linear Algebra Appl. , vol.149 , pp. 55-72
    • Ammar, G.S.1    Mehrmann, V.2
  • 2
    • 0001874303 scopus 로고
    • A multishift algorithm for the numerical solution of algebraic Riccati equations
    • Ammar, G.S., Benner, P., Mehrmann, V. (1993): A multishift algorithm for the numerical solution of algebraic Riccati equations. Electr. Trans. Num. Anal. 1, 33-48
    • (1993) Electr. Trans. Num. Anal. , vol.1 , pp. 33-48
    • Ammar, G.S.1    Benner, P.2    Mehrmann, V.3
  • 4
    • 0040483956 scopus 로고    scopus 로고
    • HAMEV and SQRED: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices using Van Loan's square reduced method
    • Fak. Mathematik, f., TU Chemnitz-Zwickau, 09107 Chemnitz, FRG Available as SFB393_96-06. ps via anonymous ftp from ftp. tu-chemnitz. de, directory /pub/Local/mathematik/Benner
    • Benner, P., Byers, R., Barth, E. (1996): HAMEV and SQRED: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices using Van Loan's square reduced method. Technical Report SFB393/96-06, Fak. Mathematik, f., TU Chemnitz-Zwickau, 09107 Chemnitz, FRG Available as SFB393_96-06. ps via anonymous ftp from ftp. tu-chemnitz. de, directory /pub/Local/mathematik/Benner.
    • (1996) Technical Report SFB393/96-06
    • Benner, P.1    Byers, R.2    Barth, E.3
  • 5
    • 0003418313 scopus 로고
    • A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case
    • Fak. Mathematik, f., TU Chemnitz-Zwickau, 09107 Chemnitz, FRG Available as SPC95_22. ps via anonymous ftp from ftp. tu-chemnitz. de, directory /pub/Local/mathematik/Benner
    • Benner, P., Laub, A., Mehrmann, V. (1995): A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case. Technical Report SPC 95_22, Fak. Mathematik, f., TU Chemnitz-Zwickau, 09107 Chemnitz, FRG Available as SPC95_22. ps via anonymous ftp from ftp. tu-chemnitz. de, directory /pub/Local/mathematik/Benner.
    • (1995) Technical Report SPC 95_22
    • Benner, P.1    Laub, A.2    Mehrmann, V.3
  • 6
    • 0026987622 scopus 로고
    • The periodic Schur decomposition; algorithms and applications
    • Bojanczyk, A., Golub, G.H., Van Dooren, P. (1992): The periodic Schur decomposition; algorithms and applications. In Proc. SPIE Conference, vol. 1770, pp. 31-42
    • (1992) Proc. SPIE Conference , vol.1770 , pp. 31-42
    • Bojanczyk, A.1    Golub, G.H.2    Van Dooren, P.3
  • 7
    • 38249039967 scopus 로고
    • Matrix factorization for symplectic QR-like methods
    • Bunse-Gerstner, A. (1986): Matrix factorization for symplectic QR-like methods. Linear Algebra Appl. 83, 49-77
    • (1986) Linear Algebra Appl. , vol.83 , pp. 49-77
    • Bunse-Gerstner, A.1
  • 9
    • 0004236492 scopus 로고
    • Johns Hopkins University Press, Baltimore, second edition
    • Golub, G.H., Van Loan, C.F. (1989): Matrix Computations. Johns Hopkins University Press, Baltimore, second edition
    • (1989) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 10
    • 0039298867 scopus 로고
    • An extension of the QR algorithm for a sequence of matrices
    • ECE Dept., University of California, Santa Barbara, CA
    • Hench, J.J., Laub, A.J. (1992): An extension of the QR algorithm for a sequence of matrices. Technical Report CCEC-92-0829, ECE Dept., University of California, Santa Barbara, CA
    • (1992) Technical Report CCEC-92-0829
    • Hench, J.J.1    Laub, A.J.2
  • 11
    • 0028447254 scopus 로고
    • Numerical solution of the discrete-time periodic Riccati equation
    • Hench, J.J., Laub, A.J. (1994): Numerical solution of the discrete-time periodic Riccati equation. IEEE Trans. Automat. Control 39, 1197-1210
    • (1994) IEEE Trans. Automat. Control , vol.39 , pp. 1197-1210
    • Hench, J.J.1    Laub, A.J.2
  • 13
    • 0018681625 scopus 로고
    • A Schur method for solving algebraic Riccati equations
    • Laub, A.J. (1979): A Schur method for solving algebraic Riccati equations. IEEE Trans. Automat. Control AC-24, 913-921 (See also Proc. 1978 CDC (Jan. 1979), pp. 60-65)
    • (1979) IEEE Trans. Automat. Control AC-24 , pp. 913-921
    • Laub, A.J.1
  • 14
    • 0018681625 scopus 로고
    • Jan.
    • Laub, A.J. (1979): A Schur method for solving algebraic Riccati equations. IEEE Trans. Automat. Control AC-24, 913-921 (See also Proc. 1978 CDC (Jan. 1979), pp. 60-65)
    • (1979) Proc. 1978 CDC , pp. 60-65
  • 15
    • 0039298862 scopus 로고
    • Algebraic aspects of generalized eigenvalue problems for solving Riccati equations
    • Byrnes, C.I., Lindquist, A. (eds.) Elsevier (North-Holland)
    • Laub, A.J. (1986): Algebraic aspects of generalized eigenvalue problems for solving Riccati equations. In Byrnes, C.I., Lindquist, A. (eds.) Computational and Combinatorial Methods in Systems Theory, pp. 213-227. Elsevier (North-Holland)
    • (1986) Computational and Combinatorial Methods in Systems Theory , pp. 213-227
    • Laub, A.J.1
  • 16
    • 0002756084 scopus 로고
    • Invariant subspace methods for the numerical solution of Riccati equations
    • Bittanti, S., Laub, A.J., Willems, J.C. (eds.) Springer-Verlag, Berlin
    • Laub, A.J. (1991): Invariant subspace methods for the numerical solution of Riccati equations. In Bittanti, S., Laub, A.J., Willems, J.C. (eds.) The Riccati Equation, pp. 163-196. Springer-Verlag, Berlin
    • (1991) The Riccati Equation , pp. 163-196
    • Laub, A.J.1
  • 17
    • 0000603860 scopus 로고
    • A new method for computing the closed loop eigenvalues of a discrete-time algebraic Riccati equation
    • Lin, W.-W. (1987): A new method for computing the closed loop eigenvalues of a discrete-time algebraic Riccati equation. Linear Algebra Appl. 6, 157-180
    • (1987) Linear Algebra Appl. , vol.6 , pp. 157-180
    • Lin, W.-W.1
  • 19
    • 21344456693 scopus 로고    scopus 로고
    • A step toward a unified treatment of continuous and discrete time control problems
    • Mehrmann, V. (1996): A step toward a unified treatment of continuous and discrete time control problems. Linear Algebra Appl. 241-243, 749-779
    • (1996) Linear Algebra Appl. , vol.241-243 , pp. 749-779
    • Mehrmann, V.1
  • 20
    • 0000356673 scopus 로고
    • An algorithm for generalized matrix eigenvalue problems
    • Moler, C.B., Stewart, G.W. (1973): An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10, 241-256
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 241-256
    • Moler, C.B.1    Stewart, G.W.2
  • 21
    • 49049146869 scopus 로고
    • A Schur decomposition for Hamiltonian matrices
    • Paige, C.C., Van Loan, C.F. (1981): A Schur decomposition for Hamiltonian matrices. Linear Algebra Appl. 14, 11-32
    • (1981) Linear Algebra Appl. , vol.14 , pp. 11-32
    • Paige, C.C.1    Van Loan, C.F.2
  • 22
    • 21144481132 scopus 로고
    • On computing the eigenvalues of a symplectic pencil
    • Patel, R.V. (1993): On computing the eigenvalues of a symplectic pencil. Linear Algebra Appl. 188/189:591-611 (See also: Proc. CDC-31, Tuscon, AZ, 1992, pp. 1921-1926)
    • (1993) Linear Algebra Appl. , vol.188-189 , pp. 591-611
    • Patel, R.V.1
  • 23
    • 21144481132 scopus 로고
    • Tuscon, AZ
    • Patel, R.V. (1993): On computing the eigenvalues of a symplectic pencil. Linear Algebra Appl. 188/189:591-611 (See also: Proc. CDC-31, Tuscon, AZ, 1992, pp. 1921-1926)
    • (1992) Proc. CDC-31 , pp. 1921-1926
  • 24
    • 0026882267 scopus 로고
    • An updating algorithm for subspace tracking
    • Stewart, G.W. (1992): An updating algorithm for subspace tracking. IEEE Trans. Signal Proc. 40, 1535-1541
    • (1992) IEEE Trans. Signal Proc. , vol.40 , pp. 1535-1541
    • Stewart, G.W.1
  • 26
    • 0040130684 scopus 로고
    • Updating a rank revealing ULV decomposition
    • Stewart, G.W. (1993): Updating a rank revealing ULV decomposition. SIAM J. Matrix Anal. Appl. 4, 494-499
    • (1993) SIAM J. Matrix Anal. Appl. , vol.4 , pp. 494-499
    • Stewart, G.W.1
  • 27
    • 0000059741 scopus 로고
    • A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
    • Van Loan, C.F. (1984): A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix. Linear Algebra Appl. 16, 233-251
    • (1984) Linear Algebra Appl. , vol.16 , pp. 233-251
    • Van Loan, C.F.1
  • 28
    • 0039298866 scopus 로고    scopus 로고
    • Personal communcication
    • Varga, A. (1996): Personal communcication
    • (1996)
    • Varga, A.1


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