Shifted power method for computing tensor eigenpairs.
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.
- Research Organization:
- Sandia National Laboratories
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1005408
- Report Number(s):
- SAND2010-6131
- Country of Publication:
- United States
- Language:
- English
Similar Records
Shifted power method for computing tensor eigenvalues.
An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
Uniform accuracy of eigenpairs from a shift-invert Lanczos method.
Conference
·
Thu Jul 01 00:00:00 EDT 2010
·
OSTI ID:1021585
An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
Journal Article
·
Wed Dec 10 23:00:00 EST 2014
· SIAM Journal on Matrix Analysis and Applications
·
OSTI ID:1126939
Uniform accuracy of eigenpairs from a shift-invert Lanczos method.
Journal Article
·
Thu Mar 31 23:00:00 EST 2005
· Proposed for publication in the SIAM Journal on Matrix Analysis and Applications Special Issue on Accurate Solution of Eigenvalue P.
·
OSTI ID:972461