An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
نویسندگان
چکیده
منابع مشابه
An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
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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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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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: 2014
ISSN: 0895-4798,1095-7162
DOI: 10.1137/140951758