Continuation Methods for Computing Z-/H-eigenpairs of Nonnegative Tensors
For researchers in tensor computation and eigenvalue problems, this provides a theoretically guaranteed algorithm for finding nonnegative eigenpairs, with a novel parity result.
The paper presents a homotopy continuation method guaranteed to compute nonnegative Z-/H-eigenpairs of nonnegative tensors, and proves via degree analysis that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. Numerical results demonstrate the method's effectiveness.
In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.