Shifted Power Method for Computing Tensor Eigenpairs
نویسندگان
چکیده
منابع مشابه
Shifted Power Method for Computing Tensor Eigenpairs
Abstract. Recent work on eigenvalues and eigenvectors for tensors of order m ≥ 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Axm−1 = λx subject to ‖x‖ = 1, which is closely related to optimal rank-1 approximation of a symm...
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Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416–422]. Given mth-order, n-dimensional realvalued symmetric tensors A and B, the goal is to find λ ∈ R and x ∈ Rn,x = 0 such that Axm−1 = λBxm−1. Different choices ...
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Let m,m′, n be positive integers such that m 6= m′. Let A be an mth order ndimensional tensor and B be an m′th order n-dimensional tensor. λ ∈ C is called a B-eigenvalue of A if Axm−1 = λBxm−1, Bxm = 1 for some x ∈ C\{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. ...
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Article history: Received 29 November 2007 Accepted 9 June 2008 Available online 17 June 2008
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2011
ISSN: 0895-4798,1095-7162
DOI: 10.1137/100801482