Shifted Power Method for Computing Tensor Eigenpairs - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 hasbeen motivated by applications in blind source separation, magnetic resonanceimaging, molecular conformation, and more. In this paper, we consider methodsfor computing real symmetric-tensor eigenpairs of the form Ax^{m-1} = \lambda xsubject to ||x||=1, which is closely related to optimal rank-1 approximation ofa symmetric tensor. Our contribution is a shifted symmetric higher-order powermethod SS-HOPM, which we show is guaranteed to converge to a tensoreigenpair. SS-HOPM can be viewed as a generalization of the power iterationmethod for matrices or of the symmetric higher-order power method.Additionally, using fixed point analysis, we can characterize exactly whicheigenpairs can and cannot be found by the method. Numerical examples arepresented, including examples from an extension of the method to findingcomplex eigenpairs.



Author: Tamara G. Kolda, Jackson R. Mayo

Source: https://arxiv.org/







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