An Alternating Shifted Inverse Power Method for the Extremal Eigenvalues of Fourth-Order Partially Symmetric Tensors.

Extremal M-eigenvalues of fourth-order partially symmetric tensors play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics. In this paper, we propose an alternating shifted inverse power method for computing the extremal M-eigenvalues of fourth-order partially symmetric tensors. The proposed algorithm is simple to operate and easy to understand for convergence analysis. Numerical experiments show the effectiveness of the proposed method.