Singular values of a real rectangular tensor
Access Status
Authors
Date
2010Type
Metadata
Show full item recordAbstract
Real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we systematically study properties of singular values of a real rectangular tensor, and give an algorithm to find the largest singular value of a nonnegative rectangular tensor. Numerical results show that the algorithm is efficient.
Citation
Source Title
Department
Remarks
NOTICE: This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications [370, 1, 2010] DOI 10.1016/j.jmaa.2010.04.037
Collections
Related items
Showing items related by title, author, creator and subject.
-
Zhou, Guanglu; Caccetta, Louis; Qi, L. (2013)In this paper, we present an iterative algorithm for computing thelargest singular value of a nonnegative rectangular tensor.We establishthe convergence of this algorithm for any irreducible nonnegativerectangular tensor.
-
Zhang, L.; Qi, L.; Zhou, Guanglu (2014)We introduce M-tensors. This concept extends the concept of M-matrices. We denote Z-tensors as the tensors with nonpositive off-diagonal entries. We show that M-tensors must be Z-tensors and the maximal diagonal entry ...
-
Paszynska, A.; Jopek, K.; Banas, K.; Paszynski, M.; Gurgul, P.; Lenerth, A.; Nguyen, D.; Pingali, K.; Dalcin, L.; Calo, Victor (2015)This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. ...