Estimates for the joint spectral radius

Applied Mathematics and Computation

Volumn 172, Issue 1, 2006, Pages 332-348

  Zhou, Xinlong ^a,b  

^a CHINA JILIANG UNIVERSITY   (China)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Joint spectral radius; Trace; Two scale dilation equation; Wavelet

Indexed keywords

COMPUTATIONAL METHODS; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

JOINT SPECTRAL RADII; TRACES; TWO-SCALE DILATION EQUATIONS; WAVELETS;

SPECTRUM ANALYZERS;

EID: 31144467253     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.02.006     Document Type: Article

References (19)

1. M.F. Barnsley Fractals Everywhere 1988 Academic Press New York
2. M.F. Barnsley, J.H. Elton, and D.P. Hardin Recurrent iterated function systems Constr. Approx. 5 1989 3 31
3. M.A. Berger, and Y. Wang Bounded semigroups of matrices Linear Algebra Appl. 166 1992 21 27
4. M. Bröker, and X. Zhou Characterization of continuous, four-coefficient scaling functions via matrix spectral radius SIAM J. Matrix Anal. Appl. 22 2000 242 257
5. A.S. Cavaretta, W. Dahmen, and C.A. Micchelli Stationary Subdivision Mem. Am. Math. Soc. 453 1991
6. Q. Chen, and X. Zhou Characterization of joint spectral radius via trace Linear Algebra Appl. 315 2000 175 188
7. A. Cohen, and Ondelettes, analyses multirésolutions et filtres miroirs en quadrature Ann. Inst. H. Poincare 7 1990 57 61
8. D. Colella, and C. Heil The characterization of continuous, four-coefficient scaling functions and wavelets IEEE Trans. Inform. Theory 38 1992 876 881
9. D. Colella, and C. Heil Characterizations of scaling functions: continuous solutions SIAM J. Matrix Anal. Appl. 15 1994 496 518
10. I. Daubechies, and J.C. Lagarias Two-scale difference equations II. Infinite matrix products, local regularity bounds and fractals SIAM J. Math. Anal. 23 1992 1031 1079
11. I. Daubechies, and J.C. Lagarias Sets of matrices all infinite products of which converge Linear Algebra Appl. 162 1992 227 263
12. T.N.T. Goodman, C.A. Micchelli, and J.D. Ward Spectral radius formulas for subdivision operators Recent Advances in Wavelet Analysis, Wavelet Anal. Appl. vol. 3 1994 Academic Press Boston, MA 335 360
13. G. Gripenberg Computing the joint spectral radius Linear Algebra Appl. 234 1996 43 60
14. C. Heil, and D. Colella Dilation equation and the smoothness of compactly supported wavelets J.L. Benedetto M.W. Frazier Wavelets: Mathematics and Applications 1994 CRC Press Boca Raton 163 201
15. C. Heil, and G. Strang Continuity of the joint spectral radius: application to wavelets A. Bojanczyk G. Cybenko Linear Algebra for Signal Processing IMA Vol. Math. Appl. 1995 Springer-Verlag New York
16. M. Maesumi An efficient lower bound for the generalized spectral radius of a set of matrices Linear Algebra Appl. 240 1996 1 7
17. C.A. Micchelli, and H. Prautzsch Uniform refinement of curves Linear Algebra Appl. 114-115 1989 841 870
18. G.C. Rota, and G. Strang A note on the joint spectral radius Indog. Math. 22 1960 379 381
19. 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 Syst. 10 1997 31 41