Lifted polytope methods for computing the joint spectral radius
(2014) SIAM Journal on Matrix Analysis and Applications — Vol. 35, n° 2, p. 391-410 (2014)
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- Abstract
- 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.
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Jungers, R., Cicone, A., & Guglielmi, N. (2014). Lifted polytope methods for computing the joint spectral radius. SIAM Journal on Matrix Analysis and Applications, 35(2), 391-410. https://doi.org/10.1137/130907811 (Original work published 2014)