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dc.contributor.authorBrazell, Michael
dc.date2013-01-01
dc.date.accessioned2018-06-10T21:41:16Z
dc.date.available2018-06-10T21:41:16Z
dc.description©2013 Society for Industrial and Applied Mathematics.
dc.description.abstractHigher 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.
dc.identifierhttp://repository.uwyo.edu/mechanical_facpub/1
dc.identifierhttp://repository.uwyo.edu/cgi/viewcontent.cgi?article=1000&context=mechanical_facpub
dc.identifier.doi10.1137/100804577
dc.identifier.urihttps://hdl.handle.net/20.500.11919/1591
dc.languageEnglish
dc.publisherUniversity of Wyoming. Libraries
dc.sourceMechanical Engineering Faculty Publications
dc.subjectLeastsquares method polynomial; Multilinear system; Tensor and matrix inversions; Tensor decomposition
dc.subjectEngineering
dc.titleSolving Multilinear Systems via Tensor Inversion
dc.typeArticle
dcterms.title.journalSIAM Journal on Matrix Analysis and Applications


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