On accuracy of approximation of the spectral radius by the Gelfand formula |
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Authors: | Victor Kozyakin |
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Institution: | aInstitute for Information Transmission Problems, Russian Academy of Sciences, Bolshoj Karetny lane 19, Moscow 127994 GSP-4, Russia |
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Abstract: | The famous Gelfand formula ρ(A)=limsupn→∞An1/n for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is substantially restricted by a lack of estimates for the rate of convergence of the quantities An1/n to ρ(A). In the paper this deficiency is made up to some extent. By using the Bochi inequalities we establish explicit computable estimates for the rate of convergence of the quantities An1/n to ρ(A). The obtained estimates are then extended for evaluation of the joint spectral radius of matrix sets. |
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Keywords: | Infinite matrix products Generalized spectral radius Joint spectral radius |
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