On accuracy of approximation of the spectral radius by the Gelfand formula
نویسنده
چکیده
The famous Gelfand formula ρ(A) = lim supn→∞ ‖A ‖ 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 ‖A‖ 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 ‖A‖ to ρ(A). The obtained estimates are then extended for evaluation of the joint spectral radius of matrix sets. PACS number 02.10.Ud; 02.10.Yn MSC 2000: 15A18; 15A60
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تاریخ انتشار 2009