Computing tensor Z-eigenpairs via an alternating direction method

Abstract

Tensor eigenproblems have wide applications in blind source separation, magnetic resonance imaging, and molecular conformation. In this study, we explore an alternating direction method for computing the largest or smallest Z-eigenvalue and corresponding eigenvector of an even-order symmetric tensor. The method decomposes a tensor Z-eigenproblem into a series of matrix eigenproblems that can be readily solved using off-the-shelf matrix eigenvalue algorithms. Our numerical results show that, in most cases, the proposed method converges over two times faster and could determine extreme Z-eigenvalues with 20–50% higher probability than a classical power method-based approach.

Keywords

• Higher-order tensor
• Z-eigenvalues
• Power method
• Alternating direction method