G. Gripenberg. Computering the joint spectral radius. Linear Algebra and its Applications, (234):43--60, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... the joint spectral radius of the associated linear operators (T 0 ) jk = 2j k 1 and (T 1 ) jk = 2j k reduced to a certain invariant subspace E, we obtain the smoothness values 1:068 and 1:701 in terms of the H older exponent (these techniques are discussed in detail in[DL92] and [Gri96]) To obtain better smoothness results, one could give up one zero order of (by adding 2 g 4;3 ) and use this degree of freedom to nd better lters. Another wish could be the property, that the coecients are rationals (as in the easy case) because this can reduce the computational ....

Gustaf Gripenberg. Computing the Joint Spectral Radius. Linear Algebra and its Applications, 234:43-60, 1996.

.... [13] and [20] In particular equality between the joint and generalized spectral radius and the largest Lyapunov exponent have been shown, three quantities that characterize exponential stability of (2) Methods for the calculation of the generalized spectral radius have been discussed in [1] [7] and [14] These approaches have in common that they are based on the calculation of ever longer matrix products and evaluating norms and spectral radii of these products. In our approach the maximal Lyapunov exponent is formulated as the optimal value of an optimal control problem on the n Gamma ....

....calculation of upper and lower bounds. As the top Lyapunov exponents does not change under convexification of M these algorithms are applicable to the special case of system (3) and Assumption 2.4, when M fl = A 0 flM and M is a polygon. For this case an approximation algorithm is presented in [7], which uses (6) to obtain upper and lower bounds. It converges to a value within a predefined error bound of the generalized spectral radius. The idea is that the algorithm evaluates the norm and the spectral radius of matrix products of length t of the form A(t Gamma 1) A(0) only in the ....

G. Gripenberg. Computering the joint spectral radius. Linear Algebra and its Applications, (234):43--60, 1996.

....easily to the calculation of stability radii as it becomes the more expensive the closer the exponential growth rate is to 0. This, however, is the interesting case when stability radii are considered. Algorithms that are based on the evaluation of matrix products have been proposed by Gripenberg [13] and Maesumi [24] In our approach the maximal Lyapunov exponent is formulated as the value of an optimal control problem on the n Gamma 1 dimensional sphere. The main idea is to approximate the intrinsically hard problem of calculating maximal Lyapunov exponents by easier ones. These are the so ....

G. Gripenberg. Computing the joint spectral radius. Linear Algebra and its Applications, 234:43--60, 1996.

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G. Gripenberg. Computering the joint spectral radius. Linear Algebra and its Applications, (234):43--60, 1996.

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G. Gripenberg. Computing the joint spectral radius. Linear Algebra and its Applications, 234:43--60, 1996.

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G. Gripenberg, Computing the Joint Spectral Radius, Linear Algebra and its Applications, 234, pp.43-60, 1996.

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., Computing Hermite and Smith normal forms of triangular integer matrices. Linear Algebra and its Applications, 282:25-45, 1998.

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