110 citations · 323 across the 20 of their papers we have counts for
6 papers · 1 filter
Nonconcavity of the Spectral Radius in Levinger's Theorem
Lee Altenberg, Joel E. Cohen
Let be a nonnegative irreducible square matrix and let be its spectral radius and Perron-Frobenius eigenvalue. Levinger asserted and sever…
An Extension of the Rayleigh Quotient to the Spectral Radius of Asymmetric Nonnegative Matrices
Lee Altenberg
The Rayleigh quotient, which provides the classical variational characterization of the spectral radius of Hermitian matrices, can be extended to nonsymmetric nonnegative irreducib…
On the Ordering of Spectral Radius Product r(A) r(AD) Versus r(A^2 D) and Related Applications
Lee Altenberg
For a nonnegative matrix A and real diagonal matrix D, two known inequalities on the spectral radius, r(A^2 D^2) >= r(AD)^2 and r(A) r(A D^2) >= r(AD)^2, leave open the question of…
A Sharpened Condition for Strict Log-Convexity of the Spectral Radius via the Bipartite Graph
Lee Altenberg
Friedland (1981) showed that for a nonnegative square matrix A, the spectral radius r(e^D A) is a log-convex functional over the real diagonal matrices D. He showed that for fully…
Resolvent Positive Linear Operators Exhibit the Reduction Phenomenon
Lee Altenberg
The spectral bound, s(a A + b V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in b \in R. This is…
Karlin Theory On Growth and Mixing Extended to Linear Differential Equations
Lee Altenberg
Karlin's (1982) Theorem 5.2 shows that linear systems alternating between growth and mixing phases have lower asymptotic growth with greater mixing. Here this result is extended to…