메뉴 건너뛰기




Volumn 285, Issue 1-3, 1998, Pages 81-105

Where is the nearest non-regular pencil?

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0040716242     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)10122-2     Document Type: Article
Times cited : (51)

References (45)
  • 3
    • 0003100869 scopus 로고    scopus 로고
    • An improved algorithm for the computation of Kronecker's canonical form of a singular pencil
    • T. Beelen, P.M. Van Dooren, An improved algorithm for the computation of Kronecker's canonical form of a singular pencil, Linear Algebra Appl. 105 (1998) 9-65.
    • (1998) Linear Algebra Appl. , vol.105 , pp. 9-65
    • Beelen, T.1    Van Dooren, P.M.2
  • 5
    • 0001847718 scopus 로고
    • Regularization of descriptor systems by derivative and proportional state feedback
    • A. Bunse-Gerstner, V. Mehrmann, N.K. Nichols, Regularization of descriptor systems by derivative and proportional state feedback, SIAM J. Matrix Anal. Appl. 13 (1992) 46-67.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 46-67
    • Bunse-Gerstner, A.1    Mehrmann, V.2    Nichols, N.K.3
  • 7
    • 0031094265 scopus 로고    scopus 로고
    • Descriptor systems without controllability at infinity
    • R. Byers, T. Geerts, V. Mehrmann, Descriptor systems without controllability at infinity, SIAM J. Control Optim. 35 (1997) 462-479.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 462-479
    • Byers, R.1    Geerts, T.2    Mehrmann, V.3
  • 8
    • 0030834983 scopus 로고    scopus 로고
    • Regularization of linear descriptor systems with variable coefficients
    • R. Byers, P. Kunkel, V. Mehrmann, Regularization of linear descriptor systems with variable coefficients, SIAM J. Control Optim. 35 (1997) 117-133.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 117-133
    • Byers, R.1    Kunkel, P.2    Mehrmann, V.3
  • 9
    • 4644340124 scopus 로고
    • On the stability radius of generalized state-space systems
    • R. Byers, N.K. Nichols, On the stability radius of generalized state-space systems, Linear Algebra Appl. 188/189 (1993) 113-134.
    • (1993) Linear Algebra Appl. , vol.188-189 , pp. 113-134
    • Byers, R.1    Nichols, N.K.2
  • 11
    • 0001345156 scopus 로고
    • On condition numbers and the distance to the nearest ill-posed problem
    • J.W. Demmel, On condition numbers and the distance to the nearest ill-posed problem, Numer. Math. 51 (1987) 251-289.
    • (1987) Numer. Math. , vol.51 , pp. 251-289
    • Demmel, J.W.1
  • 12
    • 0039690914 scopus 로고
    • Technical Report UMINF-118.84, ISSN 0348-0542, Institute of Information Processing, Umea University, S-901 87 Umea
    • J.W. Demmel, B. Kågström, Stable eigendecompositions of matrix pencils A - zB, Technical Report UMINF-118.84, ISSN 0348-0542, Institute of Information Processing, Umea University, S-901 87 Umea, 1984.
    • (1984) Stable Eigendecompositions of Matrix Pencils A - zB
    • Demmel, J.W.1    Kågström, B.2
  • 13
    • 45949117656 scopus 로고
    • Computing stable eigendecompositions of matrix pencils
    • J.W. Demmel, B. Kågström, Computing stable eigendecompositions of matrix pencils, Linear Algebra Appl. 88/89 (1987) 139-186.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 139-186
    • Demmel, J.W.1    Kågström, B.2
  • 14
    • 0001213158 scopus 로고
    • Accurate solutions of ill-posed problems in control theory
    • J.W. Demmel, B. Kågström, Accurate solutions of ill-posed problems in control theory, SIAM J. Matrix Anal. Appl. 9 (1988) 126-145.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 126-145
    • Demmel, J.W.1    Kågström, B.2
  • 15
    • 0027608731 scopus 로고
    • The generalized schur decomposition of an arbitrary pencil A - λB; robust software with error bounds and applications, part I: Theory and algorithms
    • J.W. Demmel, B, Kågström, The generalized Schur decomposition of an arbitrary pencil A - λB; Robust software with error bounds and applications, Part I: Theory and algorithms, ACM Trans. Math. Software 19 (2) (1993) 160-174.
    • (1993) ACM Trans. Math. Software , vol.19 , Issue.2 , pp. 160-174
    • Demmel, J.W.1    Kågström, B.2
  • 16
    • 0027609950 scopus 로고
    • The generalized schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applications, part II: Software and applications
    • J.W. Demmel, B. Kågström, The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applications, Part II: Software and applications, ACM Trans. Math. Software 19 (2) (1993) 175-201.
    • (1993) ACM Trans. Math. Software , vol.19 , Issue.2 , pp. 175-201
    • Demmel, J.W.1    Kågström, B.2
  • 17
    • 0039055987 scopus 로고    scopus 로고
    • The set of 2-by-3 matrix pencils - Kronecker structures and their transitions under perturbations
    • E. Elmroth, B. Kågström, The set of 2-by-3 matrix pencils - Kronecker structures and their transitions under perturbations, SIAM J. Matrix Anal. Appl. 17 (1) (1996) 1-34.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.1 , pp. 1-34
    • Elmroth, E.1    Kågström, B.2
  • 20
    • 0000394779 scopus 로고
    • The QR transformation: A unitary analogue to the LR transformation, parts I and II
    • J.G.F. Francis, The QR transformation: A unitary analogue to the LR transformation, parts I and II, Comput. J. 4 (265 272) (1961) 332-345.
    • (1961) Comput. J. , vol.4 , Issue.265-272 , pp. 332-345
    • Francis, J.G.F.1
  • 22
    • 0042178923 scopus 로고
    • Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant linear systems: The general case
    • T. Geerts, Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant linear systems: The general case, Linear Algebra Appl. 181 (1993) 111-130.
    • (1993) Linear Algebra Appl. , vol.181 , pp. 111-130
    • Geerts, T.1
  • 24
    • 0000803444 scopus 로고
    • The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate
    • G.H. Golub, V. Pereyra, The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM J. Numer. Anal. 10 (1973) 413-432.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 413-432
    • Golub, G.H.1    Pereyra, V.2
  • 26
    • 0000652188 scopus 로고
    • Unitary triangularization of a nonsymmetric matrix
    • A.S. Householder, Unitary triangularization of a nonsymmetric matrix, J. Assoc. Comput. Mach. 5 (1958) 339-342.
    • (1958) J. Assoc. Comput. Mach. , vol.5 , pp. 339-342
    • Householder, A.S.1
  • 27
    • 0000169752 scopus 로고
    • RGSVD - An algorithm for computing the Kronecker structure and reducing subspaces of singular A - λB pencils
    • B. Kågström, RGSVD - an algorithm for computing the Kronecker structure and reducing subspaces of singular A - λB pencils, SIAM J. Sci. Statist. Comput. 7 (1986) 185-211.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 185-211
    • Kågström, B.1
  • 28
    • 0016450838 scopus 로고
    • A variable projection method for solving separable nonlinear least squares problems
    • L. Kaufman, A variable projection method for solving separable nonlinear least squares problems, BIT 15 (1975) 49-57.
    • (1975) BIT , vol.15 , pp. 49-57
    • Kaufman, L.1
  • 31
    • 0016034779 scopus 로고
    • Efficient implementation of a variable projection algorithm for nonlinear least squares problems
    • F. Krogh, Efficient implementation of a variable projection algorithm for nonlinear least squares problems, Comm. ACM 17 (1974) 167-169.
    • (1974) Comm. ACM , vol.17 , pp. 167-169
    • Krogh, F.1
  • 33
    • 0039690913 scopus 로고
    • The AB-algorithm and its properties
    • V.N. Kublanovskaya, The AB-algorithm and its properties, LOMI 102 (1980) 42-60.
    • (1980) LOMI , vol.102 , pp. 42-60
    • Kublanovskaya, V.N.1
  • 34
    • 0001644871 scopus 로고
    • AB-algorithm and its modifications for the spectral problem of linear pencils of matrices
    • V.N. Kublanovskaya, AB-algorithm and its modifications for the spectral problem of linear pencils of matrices, Numer. Math. 43 (1984) 329-342.
    • (1984) Numer. Math. , vol.43 , pp. 329-342
    • Kublanovskaya, V.N.1
  • 35
    • 0039098712 scopus 로고    scopus 로고
    • Prime Parkway, Natick, MA, 01760, USA, info@mathworks.com
    • Matlab, version 5, The Math Works, 24 Prime Parkway, Natick, MA, 01760, USA, info@mathworks.com, 1996.
    • (1996) Matlab, Version 5, The Math Works , vol.24
  • 36
    • 0000356673 scopus 로고
    • An algorithm for generalized matrix eigenvalue problems
    • C.B. Moler, G.W. Stewart, An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal. 10 (1973) 241-256.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 241-256
    • Moler, C.B.1    Stewart, G.W.2
  • 37
    • 0021481124 scopus 로고
    • Newton-like minimization via the Lanczos method
    • S.G. Nash, Newton-like minimization via the Lanczos method, SIAM J. Numer. Anal. 21 (1984) 770-778.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 770-778
    • Nash, S.G.1
  • 38
    • 0001585735 scopus 로고
    • Preconditioning of truncated-Newton methods
    • S.G. Nash, Preconditioning of truncated-Newton methods, SIAM J. Sci. Statist. Comput. 6 (1985) 599-616.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 599-616
    • Nash, S.G.1
  • 39
    • 0015482839 scopus 로고
    • On the sensitivity of the eigenvalue problem Ax = λBx
    • G.W. Stewart, On the sensitivity of the eigenvalue problem Ax = λBx, SIAM J. Numer. Anal. 9 (1972) 669-686.
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 669-686
    • Stewart, G.W.1
  • 40
    • 0000769280 scopus 로고
    • The computation of kronecker's canonical form of a singular pencil
    • P.M. Van Dooren, The computation of Kronecker's canonical form of a singular pencil, Linear Algebra Appl. 27 (1979) 103-140.
    • (1979) Linear Algebra Appl. , vol.27 , pp. 103-140
    • Van Dooren, P.M.1
  • 42
    • 0016654742 scopus 로고
    • The combination shift QZ-algorithm
    • R.C. Ward, The combination shift QZ-algorithm, SIAM J. Numer. Anal. 12 (1975) 835-853.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 835-853
    • Ward, R.C.1
  • 44
    • 0000318599 scopus 로고
    • Linear differential equations and Kronecker's canonical form
    • C. De Boor, G. Golub (Ed.), Academic Press, New York
    • J.H. Wilkinson, Linear differential equations and Kronecker's canonical form, in: C. De Boor, G. Golub (Ed.), Recent advances in Numerical Analysis, Academic Press, New York, 1978, pp. 231-265.
    • (1978) Recent Advances in Numerical Analysis , pp. 231-265
    • Wilkinson, J.H.1
  • 45
    • 0040876964 scopus 로고
    • Kronecker's canonical form and the QZ-algorithm
    • J.H. Wilkinson, Kronecker's canonical form and the QZ-algorithm, Linear Algebra Appl. 28 (1979) 285-303.
    • (1979) Linear Algebra Appl. , vol.28 , pp. 285-303
    • Wilkinson, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.