Solving Multilinear Systems via Tensor Inversion
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 ...
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