Shifted power method for computing tensor eigenpairs.

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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 Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or ... continued below

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36 p.

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Mayo, Jackson R. & Kolda, Tamara Gibson October 1, 2010.

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Description

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 Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to fnding complex eigenpairs.

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36 p.

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  • Report No.: SAND2010-6131
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/1005408 | External Link
  • Office of Scientific & Technical Information Report Number: 1005408
  • Archival Resource Key: ark:/67531/metadc839306

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  • October 1, 2010

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Dec. 1, 2016, 7:53 p.m.

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Mayo, Jackson R. & Kolda, Tamara Gibson. Shifted power method for computing tensor eigenpairs., report, October 1, 2010; United States. (digital.library.unt.edu/ark:/67531/metadc839306/: accessed November 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.