We propose a modified Newton iteration for finding some nonnegativeZ-eigenpairs of a nonnegative tensor. When the tensor is irreducible, allnonnegative eigenpairs are known to be positive. We prove local quadraticconvergence of the new iteration to any positive eigenpair of a nonnegativetensor, under the usual assumption guaranteeing the local quadratic convergenceof the original Newton iteration. A big advantage of the modified Newtoniteration is that it seems capable of finding a nonnegative eigenpair startingwith any positive unit vector. Special attention is paid to transitionprobability tensors.
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