Discrete hungry integrable systems related to matrix eigenvalue and their local analysis by center manifold theory

In this paper, we first review the results of [8, 9] that two discrete hungry integrable
systems are related to matrix eigenvalue computation. Especially, we next clarify the existence of a center manifold for the discrete hungry Lotka-Volterra (dhLV) system. By using the center manifold theory, we prove that the solution of the dhLV system, employed in the dhLV algorithm for computing eigenvalues, exponentially converges to its equilibrium point.