University of Wyoming
FACW_ME_2013_10957162_Brazell_Michael.pdf (2.47 MB)

Solving Multilinear Systems via Tensor Inversion

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journal contribution
posted on 2021-11-15, 21:25 authored by Michael Brazell
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.







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Journal title

SIAM Journal on Matrix Analysis and Applications


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