Linear homotopy method for computing generalized tensor eigenpairs |
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Authors: | Liping Chen Lixing Han Liangmin Zhou |
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Institution: | 1.Department of Mathematics,Michigan State University,East Lansing,USA;2.Department of Mathematics,University of Michigan-Flint,Flint,USA |
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Abstract: | Let m,m′, n be positive integers such that m ≠ m′. Let A be an mth order n-dimensional tensor, and let ? be an m′th order n-dimensional tensor. λ ∈ ? is called a ?-eigenvalue of A if A xm?1 = λ?xm′?1 and ?xm′= 1 for some x ∈ ?n\{0}. In this paper, we propose a linear homotopy method for solving this eigenproblem. We prove that the method finds all isolated ?-eigenpairs. Moreover, it is easy to implement. Numerical results are provided to show the efficiency of the proposed method. |
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