On the finiteness property for rational matrices

Linear Algebra and Its Applications

Volumn 428, Issue 10, 2008, Pages 2283-2295

  Jungers, Raphaël M ^a   Blondel, Vincent D ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Finiteness property; Joint spectral radius; Optimal matrix products; Periodic optimal products

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FINITE AUTOMATA; OPTIMAL SYSTEMS; SET THEORY;

FINITENESS PROPERTIES; JOINT SPECTRAL RADIUS; OPTIMAL MATRIX PRODUCTS; PERIODIC OPTIMAL PRODUCTS;

MATRIX ALGEBRA;

EID: 40849120550     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2007.07.007     Document Type: Article

References (19)

1. Berger M.A., and Wang Y. Bounded semigroups of matrices. Linear Algebra Appl. 166 (1992) 21-27
2. Blondel V.D., and Canterini V. Undecidable problems for probabilistic automata of fixed dimension. Theory Comput. Syst. 36 3 (2003) 231-245
3. Blondel V.D., Jungers R., and Protasov V. On the complexity of computing the capacity of codes that avoid forbidden difference patterns. IEEE Trans. Inform. Theory 52 11 (2006) 5122-5127
4. Blondel V.D., Theys J., and Vladimirov A. An elementary counterexample to the finiteness conjecture. SIAM J. Matrix Anal. 24 4 (2003) 963-970
5. V.D. Blondel, J.N. Tsitsiklis, The lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate, Mathematics of Control, Signals, and Systems, vol. 10, pp. 31-40, 1997. Correction in 10, 381.
6. Blondel V.D., and Tsitsiklis J.N. The boundedness of all products of a pair of matrices is undecidable. Syst. Control Lett. 41 2 (2000) 135-140
7. Bousch T., and Mairesse J. Asymptotic height optimization for topical ifs, tetris heaps, and the finiteness conjecture. J. Math. Amer. Soc. 15 1 (2002) 77-111
8. V. Crespi, G.V. Cybenko, G. Jiang, The theory of trackability with applications to sensor networks, Technical Report TR2005-555, Dartmouth College, Computer Science, Hanover, NH, August 2005.
9. Gurvits L. Stability of discrete linear inclusions. Linear Algebra Appl. 231 (1995) 47-85
10. R. Jungers, NP-completeness of the computation of the capacity of constraints on codes, Master's thesis, Université Catholique de Louvain, 2005.
11. R. Jungers, V. Protasov, V.D. Blondel, Efficient algorithms for deciding the type of growth of products of integer matrices, in press, doi:10.1016/j.laa.2007.08.001 (this volume).
12. Kozyakin V. Structure of extremal trajectories of discrete linear systems and the finiteness conjecture. Automat. Remote Control 68 1 (2007) 174-209
13. Lagarias J.C., and Wang Y. The finiteness conjecture for the generalized spectral radius of a set of matrices. Linear Algebra Appl. 214 (1995) 17-42
14. Liberzon D., Hespanha J.P., and Morse A.S. Stability of switched systems: a lie-algebraic condition. Syst. Control Lett. 37 3 (1999) 117-122
15. B.E. Moision, A. Orlitsky, P.H. Siegel, Bounds on the rate of codes which forbid specified difference sequences, in: Proc. 1999 IEEE Global Telecommun. Conf. (GLOBECOM'99), 1999.
16. Moision B.E., Orlitsky A., and Siegel P.H. On codes that avoid specified differences. IEEE Trans. Inform. Theory 47 (2001) 433-442
17. Moision B.E., Orlitsky A., and Siegel P.H. On codes with local joint constraints. Linear Algebra Appl. 422 2-3 (2007) 442-454
18. Protasov V.Y. On the asymptotics of the partition function. Sbornik: Mathematics 191 3-4 (2000) 381-414
19. J. Theys, Joint spectral radius: theory and approximations, Ph.D. thesis, Université Catholique de Louvain, 2005.