A tensor singular values and its symmetric embedding eigenvalues

摘要

We study the connection between a tensor singular values and its symmetric embedding eigenvalues, and extend the result given in Ragnarsson and Van Loan (2011) [18]. The proofs of several lemmas in Ragnarsson and Van Loan (2011) [18] are simplified since the tensor–vector multiplication is adopted in our analysis. Furthermore, according to the connection, an iterative algorithm is proposed for finding the largest singular value of a nonnegative tensor, and numerical experiments are given to demonstrate viability of the iterative algorithm.