A descent cautious BFGS method for computing US-eigenvalues of symmetric complex tensors (Q2307757)

In this work a quasi-Newton method (a norm descent cautious BFGS method) for computing the US-eigenpairs of a symmetric complex tensor is presented. The global and superlinear convergence of this method are established. By the idea of embedding, a relation between U-eigenvalues of a general complex tensor and US-eigenvalues of its embedding tensor is established. The numerical results show that these methods are efficient in finding US-eigenvalues of a symmetric complex tensor and U-eigenvalues of a nonsymmetric complex tensor. The numerical results also show that the presented quasi-Newton method may find all the different Us-eigenvalues with high probability by running the algorithm at different random initial points many times.