Gelfand公式近似谱半径的精度
On accuracy of approximation of the spectral radius by the Gelfand formula
摘要：
著名的Gelfand矩阵谱半径公式$ρ(A)= \limsup_{n\to\infty}\|A^{n}\|^{1/n}$在各种数学构造中具有重要意义。不幸的是，该公式的适用范围基本上受到缺乏对量$\|A^{n}\|^{1/n}$到$ρ(A)$的收敛速率的估计的限制。本文在一定程度上弥补了这一不足。通过使用Bochi不等式，我们建立了明确的可计算的估计量$\|A^{n}\|^{1/n}$到$ρ(A)$的收敛速率。得到的估计，然后扩展的联合谱半径的矩阵集的评价。
英文摘要：
The famous Gelfand formula $ρ(A)= \limsup_{n\to\infty}\|A^{n}\|^{1/n}$ 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 $\|A^{n}\|^{1/n}$ 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 $\|A^{n}\|^{1/n}$ to $ρ(A)$. The obtained estimates are then extended for evaluation of the joint spectral radius of matrix sets.
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