NDLI: Solving Multilinear Systems via Tensor Inversion

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tamon, C. Navasca, C. Li, N. Brazell, M.
Copyright Year	2013
Abstract	Higher order tensor inversion is possible for even order. This is due to the fact that a tensor group endowed with the contracted product is isomorphic to the general linear group of degree $n$. With these isomorphic group structures, we derive a tensor SVD which we have shown to be equivalent to well-known canonical polyadic decomposition and multilinear SVD provided that some constraints are satisfied. Moreover, within this group structure framework, multilinear systems are derived and solved for problems of high-dimensional PDEs and large discrete quantum models. We also address multilinear systems which do not fit the framework in the least-squares sense. These are cases when there is an odd number of modes or when each mode has distinct dimension. Numerically we solve multilinear systems using iterative techniques, namely, biconjugate gradient and Jacobi methods.
Starting Page	542
Ending Page	570
Page Count	29
File Format	PDF
ISSN	08954798
DOI	10.1137/100804577
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	2
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-05-14
Access Restriction	Subscribed
Subject Keyword	Multilinear algebra, tensor products Eigenvalues, singular values, and eigenvectors multilinear system Eigenvalues, eigenvectors tensor and matrix inversions least-squares method polynomial tensor decomposition
Content Type	Text
Resource Type	Article
Subject	Analysis

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