Noda iteration for computing generalized tensor eigenpairs

In this paper, we propose the tensor Noda iteration (NI) and its inexact version for solving eigenvalue problem of a particular class pairs called generalized M-tensor pairs. A pair consists weakly irreducible nonnegative nonsingular within linear combination. It is shown that any admits unique positive with eigenvector. modified (MTNI) developed extending matrix eigenproblems. addition, method (IGTNI) Newton-Noda (GNNI) are also introduced more efficient implementations faster convergence. Under mild assumption on initial values, convergence these algorithms guaranteed. The efficiency illustrated by numerical experiments.