Jungers, Raphaël M.; Cicone, Antonio; Guglielmi, Nicola Lifted polytope methods for computing the joint spectral radius. (English) Zbl 1296.93067 SIAM J. Matrix Anal. Appl. 35, No. 2, 391-410 (2014). Summary: 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. Cited in 2 Documents MSC: 93B60 Eigenvalue problems 15A18 Eigenvalues, singular values, and eigenvectors 93C55 Discrete-time control/observation systems 37C75 Stability theory for smooth dynamical systems 90C22 Semidefinite programming 93D30 Lyapunov and storage functions Keywords:joint spectral radius; lifting methods; iterative methods; matrix semigroups; semidefinite programming; finiteness property Software:JSR PDFBibTeX XMLCite \textit{R. M. Jungers} et al., SIAM J. Matrix Anal. Appl. 35, No. 2, 391--410 (2014; Zbl 1296.93067) Full Text: DOI Link