The generalized spectral radius and extremal norms

141 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On the accuracy of the ellipsoid norm approximation of the joint spectral radius (2005, background): “A norm achieving this infimum is said to be extremal for the set (not every set of matrices possesses an extremal norm, see [21] for a discussion of this issue).”
Structure of extremal trajectories of discrete linear systems and the finiteness conjecture (2007, unknown): “These ideas were further developed in a number of publications amongst which we distinguish [ 20 ].”
The Berger-Wang formula for the Markovian joint spectral radius (2014, background): “Specifically, there is valid the following Markovian analog of Wirth’s Theorem from [15].”
ERGODIC OPTIMIZATION OF BIRKHOFF AVERAGES AND LYAPUNOV EXPONENTS (2017, background): “2 These extremal norms provide a fundamental tool in the study of the joint spectral radius: see also [65, 43].”
Continuity properties of the lower spectral radius (2013, background): “Similarly, the upper spectral radius was shown in 1995 by Heil and Strang [33] to depend continuously on the set A, and this was subsequently strengthened to Lipschitz continuity when A does not admit a common invariant subspace [37, 58] or when A admits a strictly invariant cone [43].”