User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

An experimental study of approximation algorithms for the joint spectral radius

Primary tabs

download
  • Open access
  • PDF
  • 385.87 K
Chang, Chia-Tche [UCL] Blondel, Vincent [UCL]
Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2013
Language Anglais
Journal information "Numerical Algorithms" - Vol. 64, no. 1, p. 181-202 (2013)
Peer reviewed yes
Publisher Springer New York LLC ((United States) New York)
issn 1017-1398
e-issn 1572-9265
Publication status Publié
Affiliation UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique
Links
  1. Berger Marc A., Wang Yang, Bounded semigroups of matrices, 10.1016/0024-3795(92)90267-e
  2. Blondel Vincent D., Nesterov Yurii, Computationally Efficient Approximations of the Joint Spectral Radius, 10.1137/040607009
  3. Blondel Vincent D., Nesterov Yurii, Theys Jacques, On the accuracy of the ellipsoid norm approximation of the joint spectral radius, 10.1016/j.laa.2004.06.024
  4. Blondel Vincent D., Theys Jacques, Vladimirov Alexander A., An Elementary Counterexample to the Finiteness Conjecture, 10.1137/s0895479801397846
  5. Bousch, T., Mairesse, J.: Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture. J. AMS 15(1), 77–111 (2002).
  6. Chang, C.T., Blondel, V.D.: Approximating the joint spectral radius using a genetic algorithm framework. In: Proc. 18th IFAC World Congress, Vol. 18, pp. 8681–8686. Milano, Italy (2011)
  7. Cicone Antonio, Guglielmi Nicola, Serra-Capizzano Stefano, Zennaro Marino, Finiteness property of pairs of 2×2 sign-matrices via real extremal polytope norms, 10.1016/j.laa.2009.09.022
  8. Daubechies Ingrid, Lagarias Jeffrey C., Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals, 10.1137/0523059
  9. Gripenberg Gustaf, Computing the joint spectral radius, 10.1016/0024-3795(94)00082-4
  10. Guglielmi, N., Zennaro, M.: Balanced complex polytopes and related vector and matrix norms. J. Convex Anal. 14, 729–766 (2007).
  11. Guglielmi N., Zennaro M., Finding Extremal Complex Polytope Norms for Families of Real Matrices, 10.1137/080715718
  12. Gurvits Leonid, Stability of discrete linear inclusion, 10.1016/0024-3795(95)90006-3
  13. Hare Kevin G., Morris Ian D., Sidorov Nikita, Theys Jacques, An explicit counterexample to the Lagarias–Wang finiteness conjecture, 10.1016/j.aim.2010.12.012
  14. Jungers Raphaël, The Joint Spectral Radius, ISBN:9783540959793, 10.1007/978-3-540-95980-9
  15. Jungers Raphaël M., Protasov Vladimir Y., Blondel Vincent D., Overlap-free words and spectra of matrices, 10.1016/j.tcs.2009.04.022
  16. Knuth, D.E.: The Art of Computer Programming, Volume 2, Seminumerical Algorithms. Addison-Wesley, Reading, MA (1997)
  17. Kozyakin, V.S.: Proof of a Counterexample to the Finiteness Conjecture in the Spirit of the Theory of Dynamical Systems. Preprint 1005. Weierstraß-Institut f¨ur Angewandte Analysis und Stochastik, Berlin (2005)
  18. Kozyakin V. S., Structure of extremal trajectories of discrete linear systems and the finiteness conjecture, 10.1134/s0005117906040171
  19. Kozyakin Victor, On accuracy of approximation of the spectral radius by the Gelfand formula, 10.1016/j.laa.2009.07.008
  20. Kozyakin Victor, A relaxation scheme for computation of the joint spectral radius of matrix sets, 10.1080/10236198.2010.549008
  21. Kozyakin Victor, Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets, 10.3934/dcdsb.2010.14.143
  22. Lagarias Jeffrey C., Wang Yang, The finiteness conjecture for the generalized spectral radius of a set of matrices, 10.1016/0024-3795(93)00052-2
  23. Maesumi Mohsen, An efficient lower bound for the generalized spectral radius of a set of matrices, 10.1016/0024-3795(94)00171-5
  24. Maesumi, M.: Calculating joint spectral radius of matrices and H¨older exponent of wavelets. Approx. Theory IX 2, 1–8 (1998).
  25. Moision B.E., Orlitsky A., Siegel P.H., On codes that avoid specified differences, 10.1109/18.904557
  26. Parrilo Pablo A., Jadbabaie Ali, Approximation of the joint spectral radius using sum of squares, 10.1016/j.laa.2007.12.027
  27. Protasov, V.Y.: The joint spectral radius and invariant sets of linear operators. Fundam. Prikl. Mat. 2(1), 205–231 (1996).
  28. Protasov Vladimir Y., Jungers Raphaël M., Blondel Vincent D., Joint Spectral Characteristics of Matrices: A Conic Programming Approach, 10.1137/090759896
  29. Rota Gian–Carlo, Gilbert Strang W., A note on the joint spectral radius, 10.1016/s1385-7258(60)50046-1
  30. Shorten Robert, Wirth Fabian, Mason Oliver, Wulff Kai, King Christopher, Stability Criteria for Switched and Hybrid Systems, 10.1137/05063516x
  31. Tsitsiklis John N., Blondel Vincent D., The Lyapunov exponent and joint spectral radius of pairs of matrices are hard?when not impossible?to compute and to approximate, 10.1007/bf01219774
  32. Vankeerbergen, G., Hendrickx, J., Jungers, R., Chang, C.T., Blondel, V.: The JSR Toolbox. MATLAB®Central. [Software, MATLAB® toolbox]. Files available at http://www.mathworks.com/matlabcentral/fileexchange/33202-the-jsr-toolbox (2011)
  33. Wirth Fabian, The generalized spectral radius and extremal norms, 10.1016/s0024-3795(01)00446-3
Bibliographic reference Chang, Chia-Tche ; Blondel, Vincent. An experimental study of approximation algorithms for the joint spectral radius. In: Numerical Algorithms, Vol. 64, no. 1, p. 181-202 (2013)
Permanent URL http://hdl.handle.net/2078.1/117082