An efficient randomized homotopy method to approximate eigenpairs of tensors

Abstract

Let $A\in ({\mathbb{C}}^n{)}^{\otimes p}$ be a complex tensor of order $p$. The pair $(v,\eta )\in {\mathbb{C}}^n\times \mathbb{C}$ is called an h-eigenpair of $A$, if $v\ne 0$ and it satisfies $A{v}^{p-1}={\eta }^{p-2}v$, where $A{v}^{p-1}$ is the contraction of $A$ by $v$ in all but the first modes. We describe a randomized algorithm to compute approximations of h-eigenpairs of complex tensors. Assuming random input, the average number of arithmetic operations it performs is polynomially bounded in the input size.

References in corpus (2)

• The Number of Eigenvalues of a Tensor
• Singular Values and Eigenvalues of Tensors: A Variational Approach