A sequence of lower bounds for the spectral radius of nonnegative matrices (Q1195349)

Let \(A=(a_{ij})\), \(r(A)\) and \(S(A)=(\sqrt{a_{ij}}\sqrt{a_{ji}})\) denote a nonnegative square matrix, its spectral radius and its geometric symmetrization, respectively. The author shows that \(q_ k=r(S(A^{2^ k}))^{2^{-k}}\) is a nondecreasing sequence of lower bounds of \(r(A)\) and compares \(q_ k\) with bounds given by \textit{Lilia Yu. Kolotilina} [Lower bounds for the Perron root of a nonnegative matrix. ibid. (to appear)].