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Volumn 24, Issue 4, 2003, Pages 963-970

An elementary counterexample to the finiteness conjecture

Author keywords

Finiteness conjecture; Generalized spectral radius; Joint spectral radius; Matrix semigroup; Spectral radius

Indexed keywords


EID: 0142138715     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479801397846     Document Type: Article
Times cited : (101)

References (17)
  • 1
    • 0002046992 scopus 로고
    • Bounded semigroups of matrices
    • M. BERGER AND Y. WANG, Bounded semigroups of matrices, Linear Algebra Appl., 166 (1992), pp. 21-27.
    • (1992) Linear Algebra Appl. , vol.166 , pp. 21-27
    • Berger, M.1    Wang, Y.2
  • 2
    • 0034264701 scopus 로고    scopus 로고
    • A survey of computational complexity results in systems and control
    • V. D. BLONDEL AND J. N. TSITSIKLIS, A survey of computational complexity results in systems and control, Automatica, 36 (2000), pp. 1249-1274.
    • (2000) Automatica , vol.36 , pp. 1249-1274
    • Blondel, V.D.1    Tsitsiklis, J.N.2
  • 3
    • 0009944648 scopus 로고    scopus 로고
    • The boundedness of all products of a pair of matrices is undecidable
    • V. D. BLONDEL AND J. N. TSITSIKLIS, The boundedness of all products of a pair of matrices is undecidable, Systems Control Lett., 41 (2000), pp. 135-140.
    • (2000) Systems Control Lett. , vol.41 , pp. 135-140
    • Blondel, V.D.1    Tsitsiklis, J.N.2
  • 4
    • 0036001743 scopus 로고    scopus 로고
    • Asymptotic height optimization for topical IFS, Tetris heaps and the finiteness conjecture
    • T. BOUSCH AND J. MAIRESSE, Asymptotic height optimization for topical IFS, Tetris heaps and the finiteness conjecture, J. Amer. Math. Soc., 15 (2002), pp. 77-111.
    • (2002) J. Amer. Math. Soc. , vol.15 , pp. 77-111
    • Bousch, T.1    Mairesse, J.2
  • 6
    • 33846998909 scopus 로고
    • Stability of discrete linear inclusions
    • L. GURVITS, Stability of discrete linear inclusions, Linear Algebra Appl., 231 (1995), pp. 47-85.
    • (1995) Linear Algebra Appl. , vol.231 , pp. 47-85
    • Gurvits, L.1
  • 7
    • 0001219086 scopus 로고
    • Sets of matrices all infinite products of which converge
    • I. DAUBECHIES AND J. C. LAGARIAS, Sets of matrices all infinite products of which converge, Linear Algebra Appl., 161 (1992), pp. 227-263.
    • (1992) Linear Algebra Appl. , vol.161 , pp. 227-263
    • Daubechies, I.1    Lagarias, J.C.2
  • 8
    • 20244376286 scopus 로고    scopus 로고
    • Corrigendum/addendum to "Sets of matrices all infinite products of which converge,"
    • I. DAUBECHIES AND J. C. LAGARIAS, Corrigendum/addendum to "Sets of matrices all infinite products of which converge," Linear Algebra Appl., 327 (2001), pp. 69-83.
    • (2001) Linear Algebra Appl. , vol.327 , pp. 69-83
    • Daubechies, I.1    Lagarias, J.C.2
  • 9
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 11
    • 84904781597 scopus 로고
    • Algebraic unsolvability of a problem on the absolute stability of desynchronized systems
    • V. S. KOZYAKIN, Algebraic unsolvability of a problem on the absolute stability of desynchronized systems, Automat. Remote Control, 51 (1990), pp. 754-759.
    • (1990) Automat. Remote Control , vol.51 , pp. 754-759
    • Kozyakin, V.S.1
  • 12
    • 21844487357 scopus 로고
    • The finiteness conjecture for the generalized spectral radius of a set of matrices
    • J. C. LAGARIAS AND Y. WANG, The finiteness conjecture for the generalized spectral radius of a set of matrices, Linear Algebra Appl., 214 (1995), pp. 17-42.
    • (1995) Linear Algebra Appl. , vol.214 , pp. 17-42
    • Lagarias, J.C.1    Wang, Y.2
  • 13
    • 0000719845 scopus 로고
    • A note on the joint spectral radius
    • G.-C. ROTA AND W. G. STRANG, A note on the joint spectral radius, Indag. Math., 22 (1960), pp. 379-381.
    • (1960) Indag. Math. , vol.22 , pp. 379-381
    • Rota, G.-C.1    Strang, W.G.2
  • 14
    • 0142227080 scopus 로고    scopus 로고
    • The joint spectral radius
    • Commentary by Gilbert Strang on paper number 5
    • G. STRANG, The joint spectral radius, Commentary by Gilbert Strang on paper number 5, in Collected Works of Gian-Carlo Rota, 2001; available online from http://www-math.mit.edu/̃gs.
    • (2001) Collected Works of Gian-Carlo Rota
    • Strang, G.1
  • 15
    • 0030651078 scopus 로고    scopus 로고
    • The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - When not impossible - To compute and to approximate
    • J. N. TSITSIKLIS AND V. D. BLONDEL, The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate, Math. Control Signals Systems, 10 (1997), pp. 31-40.
    • (1997) Math. Control Signals Systems , vol.10 , pp. 31-40
    • Tsitsiklis, J.N.1    Blondel, V.D.2
  • 16
    • 0034401720 scopus 로고    scopus 로고
    • Stability and paracontractivity of discrete linear inclusions
    • A. A. VLADIMIROV, L. ELSNER, AND W.-J. BEYN, Stability and paracontractivity of discrete linear inclusions, Linear Algebra Appl., 312 (2000), pp. 125-134.
    • (2000) Linear Algebra Appl. , vol.312 , pp. 125-134
    • Vladimirov, A.A.1    Elsner, L.2    Beyn, W.-J.3
  • 17
    • 31244433291 scopus 로고    scopus 로고
    • The generalized spectral radius and extremal norms
    • F. WIRTH, The generalized spectral radius and extremal norms, Linear Algebra Appl., 342 (2002), pp. 17-40.
    • (2002) Linear Algebra Appl. , vol.342 , pp. 17-40
    • Wirth, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.