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Title: 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 real-valued symmetric tensors $${\mathscr{A}}$$ and $$\boldsymbol{\mathscr{B}}$$, the goal is to find $$\lambda \in \mathbb{R}$$ and $$\mathbf{x} \in \mathbb{R}^{n}, \mathbf{x} \neq 0$$ such that $${\mathscr{A}}\mathbf{x}^{m-1} = \lambda {\mathscr{B}}\mathbf{x}^{m-1}$$. Different choices for $${\mathscr{B}}$$ yield different versions of the tensor eigenvalue problem. We present our generalized eigenproblem adaptive power (GEAP) method for solving the problem, which is an extension of the shifted symmetric higher-order power method (SS-HOPM) for finding Z-eigenpairs. A major drawback of SS-HOPM is that its performance depended on choosing an appropriate shift, but our GEAP method also includes an adaptive method for choosing the shift automatically.
Authors:
;
Publication Date:
OSTI Identifier:
1126939
Report Number(s):
SAND2014--0027J
Journal ID: ISSN 0895-4798; 493218
DOE Contract Number:
AC04-94AL85000
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM Journal on Matrix Analysis and Applications; Journal Volume: 35; Journal Issue: 4; Related Information: Proposed for publication in To be determined, pending review outcomes.
Publisher:
SIAM
Research Org:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING