Lifted Polytope Methods for Computing the Joint Spectral Radius
Raphaël M. Jungers, Antonio Cicone, Nicola Guglielmi · SIAM Journal on Matrix Analysis and Applications · 2014
We present new methods for computing the joint spectral radius of finite sets of matrices. The methods build on two ideas that previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of these two ideas allows us to introduce a pruning algorithm which can importantly reduce the computational burden. We prove several theoretical properties of our methods, such as finiteness computational result which extends a known result for unlifted sets of matrices, and provide numerical examples of their good behavior.