in this article we consider relative iteration of entire functions and studycomparative growth of the maximum term of iterated entire functions withthat of the maximum term of the related functions.

The Perron-Frobenius Theorem for irreducible higher order tensors does not guarantee simplicity of the unique positive eigenvalue nor does it guarantee the unique positive eigenvalue is strictly larger than the modulus of any other eigenvalue. Irreducibility of a tensor in relation to a graph is studied. A higher order tensor is essentially positive if it takes the positive cone to its interior...

In this article, by extending the method of [AC] we prove a sharp estimate on the expansion modulus of the gradient of the logarithm of the parabolic kernel to the Schördinger operator with convex potential on a bounded convex domain. The result improves an earlier work of Brascamp-Lieb which asserts the log-concavity of the parabolic kernel. We also give an alternate proof to a corresponding e...

In this paper, we propose an inexact inverse iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We prove that this approach preserves the lin...