Linear homotopy method for computing generalized tensor eigenpairs

摘要

Let m,m', n be positive integers such that m not equal m'. Let A be an mth order n-dimensional tensor, and let a"notsign be an m'th order n-dimensional tensor. lambda a a", is called a a"notsign-eigenvalue of A if A x (m-1) = lambda a"notsignx (m'-1) and a"notsignx m'= 1 for some x a a",(n){0}. In this paper, we propose a linear homotopy method for solving this eigenproblem. We prove that the method finds all isolated a"notsign-eigenpairs. Moreover, it is easy to implement. Numerical results are provided to show the efficiency of the proposed method.