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 like a finiteness computational result which extends a known result for unlifted sets of matrices, and provide numerical examples of their good behaviour.
Lifted Polytope Methods for Computing the Joint Spectral Radius.
GUGLIELMI N
2014-01-01
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 like a finiteness computational result which extends a known result for unlifted sets of matrices, and provide numerical examples of their good behaviour.File in questo prodotto:
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