메뉴 건너뛰기




Volumn 28, Issue 1, 2006, Pages 285-300

Direct eigenvalue reordering in a product of matrices in periodic schur form

Author keywords

Eigenvalue reordering; Extended periodic real schur form; K periodic Sylvester equation; Periodic eigenvalue problem; Product of K periodic matrix sequence

Indexed keywords

COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; PROBLEM SOLVING; TIME VARYING SYSTEMS;

EID: 33847123977     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/05062490X     Document Type: Article
Times cited : (19)

References (32)
  • 2
    • 43949169431 scopus 로고
    • On swapping diagonal blocks in real Schur form
    • Z. BAI AND J. W. DEMMEL, On swapping diagonal blocks in real Schur form, Linear Algebra Appl., 186 (1993), pp. 73-95.
    • (1993) Linear Algebra Appl , vol.186 , pp. 73-95
    • BAI, Z.1    DEMMEL, J.W.2
  • 3
    • 84976855597 scopus 로고
    • Algorithm 432 : The Solution of the Matrix Equation AX - BX = C
    • R. H. BARTELS AND G. W. STEWART, Algorithm 432 : The Solution of the Matrix Equation AX - BX = C, Comm. ACM, 8 (1972), pp. 820-826.
    • (1972) Comm. ACM , vol.8 , pp. 820-826
    • BARTELS, R.H.1    STEWART, G.W.2
  • 4
    • 0042920736 scopus 로고    scopus 로고
    • Perturbation analysis for the eigenvalue problem of a formal product of matrices
    • P. BENNER, V. MEHRMANN, AND H. XU, Perturbation analysis for the eigenvalue problem of a formal product of matrices, BIT, 42 (2002), pp. 1-43.
    • (2002) BIT , vol.42 , pp. 1-43
    • BENNER, P.1    MEHRMANN, V.2    XU, H.3
  • 6
    • 33646491344 scopus 로고
    • On propagating orthogonal transformations in a product of 2×2 triangular matrices
    • de Gruyter, New York
    • A. BOJANCZYK AND P. VAN DOOREN, On propagating orthogonal transformations in a product of 2×2 triangular matrices, in Numerical Linear Algebra, de Gruyter, New York, 1993, pp. 1-9.
    • (1993) Numerical Linear Algebra , pp. 1-9
    • BOJANCZYK, A.1    VAN DOOREN, P.2
  • 7
    • 0039715002 scopus 로고
    • Reordering diagonal blocks in the real Schur form
    • M. S. Moonen, G. H. Golub, and B. L. R. De Moor, eds, Kluwer Academic Publishers, Amsterdam
    • A. BOJANCZYK AND P. VAN DOOREN, Reordering diagonal blocks in the real Schur form, in Linear Algebra for Large Scale and Real-Time Applications, M. S. Moonen, G. H. Golub, and B. L. R. De Moor, eds., Kluwer Academic Publishers, Amsterdam, 1993, pp. 351-352.
    • (1993) Linear Algebra for Large Scale and Real-Time Applications , pp. 351-352
    • BOJANCZYK, A.1    VAN DOOREN, P.2
  • 9
    • 1842865668 scopus 로고    scopus 로고
    • Algorithms for almost block diagonal linear systems
    • G. FAIRWEATHER AND I. GLADWELL, Algorithms for almost block diagonal linear systems, SIAM Rev., 46 (2004), pp. 49-58.
    • (2004) SIAM Rev , vol.46 , pp. 49-58
    • FAIRWEATHER, G.1    GLADWELL, I.2
  • 10
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed, The Johns Hopkins University Press, Baltimore, MD
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • GOLUB, G.H.1    VAN LOAN, C.F.2
  • 11
    • 33847162931 scopus 로고    scopus 로고
    • Direct Eigenvalue Reordering in o Product of Matrices in Extended Periodic Real Schur Form
    • 05.05, Umeå University, Umeå, Sweden
    • R. GRANAT AND B. KÅGSTRÖM, Direct Eigenvalue Reordering in o Product of Matrices in Extended Periodic Real Schur Form, Report UMINF 05.05, Umeå University, Umeå, Sweden, 2005.
    • (2005) Report UMINF
    • GRANAT, R.1    KÅGSTRÖM, B.2
  • 13
    • 0028447254 scopus 로고
    • Numerical solution of the discrete-time periodic Riccati equation
    • J. J. HENCH AND A. J. LAUB, Numerical solution of the discrete-time periodic Riccati equation, IEEE Trans. Automat. Control, 39 (1994), pp. 1197-1210.
    • (1994) IEEE Trans. Automat. Control , vol.39 , pp. 1197-1210
    • HENCH, J.J.1    LAUB, A.J.2
  • 14
    • 0024143903 scopus 로고
    • Fortran codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
    • N. J. HIGHAM, Fortran codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation, ACM Trans. Math. Software, 14 (1988), pp. 381-396.
    • (1988) ACM Trans. Math. Software , vol.14 , pp. 381-396
    • HIGHAM, N.J.1
  • 16
    • 0039428375 scopus 로고
    • A direct method for reordering eigenvalues in the generalized real Schur form of a regular matrix pair (A, B)
    • M. S. Moonen, G. H. Golub, and B. L. R. De Moor, eds, Kluwer Academic Publishers, Amsterdam
    • B. KÅGSTRÖM, A direct method for reordering eigenvalues in the generalized real Schur form of a regular matrix pair (A, B), in Linear Algebra for Large Scale and Real-Time Applications, M. S. Moonen, G. H. Golub, and B. L. R. De Moor, eds., Kluwer Academic Publishers, Amsterdam, 1993, pp. 195-218.
    • (1993) Linear Algebra for Large Scale and Real-Time Applications , pp. 195-218
    • KÅGSTRÖM, B.1
  • 18
    • 0041103179 scopus 로고    scopus 로고
    • Computing eigenspaces with specified eigenvalues of a regular matrix pair (A, B) and condition estimation: Theory, algorithms, and software
    • B. KÅGSTRÖM AND P. POROMAA, Computing eigenspaces with specified eigenvalues of a regular matrix pair (A, B) and condition estimation: Theory, algorithms, and software, Numer. Algorithms, 12 (1996), pp. 369-407.
    • (1996) Numer. Algorithms , vol.12 , pp. 369-407
    • KÅGSTRÖM, B.1    POROMAA, P.2
  • 20
    • 0035501641 scopus 로고    scopus 로고
    • Perturbation analysis for the eigenproblem of periodic matrix pairs
    • W.-W. LIN AND J.-G. SUN, Perturbation analysis for the eigenproblem of periodic matrix pairs, Linear Algebra Appl., 337 (2001), pp. 157-187.
    • (2001) Linear Algebra Appl , vol.337 , pp. 157-187
    • LIN, W.-W.1    SUN, J.-G.2
  • 22
    • 33847158062 scopus 로고    scopus 로고
    • J. SREEDHAR AND P. VAN DOOREN, A Schur approach for solving some periodic matrix equations, in Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Saurer, eds., Akademie Verlag, Berlin, 1994, pp. 339-362.
    • J. SREEDHAR AND P. VAN DOOREN, A Schur approach for solving some periodic matrix equations, in Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Saurer, eds., Akademie Verlag, Berlin, 1994, pp. 339-362.
  • 23
    • 0001884632 scopus 로고
    • Algorithm 407 : HQR3 and EXCHNG: FORTRAN programs for calculating the eigenvalues of a real upper Hessenberg matrix in a prescribed order
    • G. W. STEWART, Algorithm 407 : HQR3 and EXCHNG: FORTRAN programs for calculating the eigenvalues of a real upper Hessenberg matrix in a prescribed order, ACM Trans. Math. Software, 2 (1976), pp. 275-280.
    • (1976) ACM Trans. Math. Software , vol.2 , pp. 275-280
    • STEWART, G.W.1
  • 24
    • 0001333621 scopus 로고
    • Perturbation bounds for the QR factorization of a matrix
    • G. W. STEWART, Perturbation bounds for the QR factorization of a matrix, SIAM J. Numer. Anal., 14 (1977), pp. 509-518.
    • (1977) SIAM J. Numer. Anal , vol.14 , pp. 509-518
    • STEWART, G.W.1
  • 26
    • 84976789456 scopus 로고
    • Algorithm 590 : DSUBSP and EXCHQZ: Fortran subroutines for computing deflating subspaces with specified spectrum
    • P. VAN DOOREN, Algorithm 590 : DSUBSP and EXCHQZ: Fortran subroutines for computing deflating subspaces with specified spectrum, ACM Trans. Math. Software, 8 (1982), pp. 376-382.
    • (1982) ACM Trans. Math. Software , vol.8 , pp. 376-382
    • VAN DOOREN, P.1
  • 27
    • 0031142776 scopus 로고    scopus 로고
    • Periodic Lyapunov equations: Some applications and new algorithms
    • A. VARGA, Periodic Lyapunov equations: Some applications and new algorithms, Internat. J. Control, 67 (1997), pp. 69-87.
    • (1997) Internat. J. Control , vol.67 , pp. 69-87
    • VARGA, A.1
  • 28
    • 0000804382 scopus 로고    scopus 로고
    • Balancing related methods for minimal realization of periodic systems
    • A. VARGA, Balancing related methods for minimal realization of periodic systems, Systems Control Lett., 36 (1999), pp. 339-349.
    • (1999) Systems Control Lett , vol.36 , pp. 339-349
    • VARGA, A.1
  • 29
    • 0032047407 scopus 로고    scopus 로고
    • Gradient-based approach to solve optimal periodic output feedback control problems
    • A. VARGA AND S. PIETERS, Gradient-based approach to solve optimal periodic output feedback control problems, Automatica, 45 (1998), pp. 477-481.
    • (1998) Automatica , vol.45 , pp. 477-481
    • VARGA, A.1    PIETERS, S.2
  • 32
    • 0012033691 scopus 로고
    • A collection of problems for which Gaussian elimination with partial pivoting is unstable
    • S. J. WRIGHT, A collection of problems for which Gaussian elimination with partial pivoting is unstable, SIAM J. Sci. Comput., 14 (1993), pp. 231-238.
    • (1993) SIAM J. Sci. Comput , vol.14 , pp. 231-238
    • WRIGHT, S.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.