Refined Geršhgorin disks for tensors and GH-tensors.

In this paper, exploiting the structure of tensors, the so called refined Geršhgorin disks for H-eigenvalues of tensors are introduced, which are always tighter than the classical Geršhgorin-type theorem for H-eigenvalues of tensors introduced by Qi (J Symb Comput 40:1302–1324, 2005). A sufficient condition for the positivity of even-order tensors is also given. We introduce the definition of G H -tensors, which can be viewed as a generalization of H -tensors. Moreover, an algorithm for identifying G H -tensors is also obtained. We prove that the tensor equation A x m - 1 = b has a unique positive solution if A is a strong G H + -tensor and b ∈ R n is a positive vector. [ABSTRACT FROM AUTHOR]