Lower bounds for the spectral radius of a matrix
نویسنده
چکیده
In this paper we develop lower bounds for the spectral radius of symmetric , skew{symmetric, and arbitrary real matrices. Our approach utilizes the well{known Leverrier{Faddeev algorithm for calculating the co-eecients of the characteristic polynomial of a matrix in conjunction with a theorem by Lucas which states that the critical points of a polynomial lie within the convex hull of its roots. Our results generalize and simplify a proof recently published by Tarazaga for a lower bound on the spectral radius of a symmetric positive deenite matrix. In addition, we provide new lower bounds for the spectral radius of skew{symmetric matrices. We apply these results to a problem involving the stability of xed points in recurrent neural networks.
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تاریخ انتشار 2007