  We propose a modified Newton iteration for finding some nonnegative
Z-eigenpairs of a nonnegative tensor. When the tensor is irreducible, all
nonnegative eigenpairs are known to be positive. We prove local quadratic
convergence of the new iteration to any positive eigenpair of a nonnegative
tensor, under the usual assumption guaranteeing the local quadratic convergence
of the original Newton iteration. A big advantage of the modified Newton
iteration is that it seems capable of finding a nonnegative eigenpair starting
with any positive unit vector. Special attention is paid to transition
probability tensors.
