A modified Newton iteration for finding nonnegative Z-eigenpairs of a nonnegative tensor
Provides a theoretical improvement for computing nonnegative eigenpairs of nonnegative tensors, which is relevant for tensor decomposition and Markov chain applications.
The paper proposes a modified Newton iteration for finding nonnegative Z-eigenpairs of nonnegative tensors, proving local quadratic convergence to positive eigenpairs. The method can find nonnegative eigenpairs from any positive starting vector.
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.