In this paper the problem of the computation of the joint spectral radius of a finite set of matrices is considered. We present an algorithm which, under some suitable assumptions, is able to check if a certain product in the multiplicative semigroup is spectrum maximizing. The algorithm proceeds by attempting to construct a suitable extremal norm for the family, namely a complex polytope norm. As examples for testing our technique, we first consider the set of two 2-dimensional matrices recently analyzed by Blondel, Nesterov and Theys to disprove the finiteness conjecture, and then a set of 3-dimensional matrices arising in the zero-stability analysis of the 4-step BDF formula for ordinary differential equations.

An algorithm for finding extremal polytope norms of matrix families

GUGLIELMI, NICOLA;
2008-01-01

Abstract

In this paper the problem of the computation of the joint spectral radius of a finite set of matrices is considered. We present an algorithm which, under some suitable assumptions, is able to check if a certain product in the multiplicative semigroup is spectrum maximizing. The algorithm proceeds by attempting to construct a suitable extremal norm for the family, namely a complex polytope norm. As examples for testing our technique, we first consider the set of two 2-dimensional matrices recently analyzed by Blondel, Nesterov and Theys to disprove the finiteness conjecture, and then a set of 3-dimensional matrices arising in the zero-stability analysis of the 4-step BDF formula for ordinary differential equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/7921
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