LAUSR

Let m,m′, n be positive integers such that m ≠ m′. Let A be an mth order n-dimensional tensor, and let ℬ be an m′th order n-dimensional tensor. λ ∈ ℂ is called a ℬ-eigenvalue of A if Axm−1 = λℬxm′−1 and ℬxm′= 1 for some x ∈ ℂn\{0}. In this paper, we propose a linear homotopy method for solving this eigenproblem. We prove that the method finds all isolated ℬ-eigenpairs. Moreover, it is easy to implement. Numerical results are provided to show the efficiency of the proposed method.