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dc.contributor.authorMickelin, Oscar
dc.contributor.authorKaraman, Sertac
dc.date.accessioned2021-10-27T20:30:05Z
dc.date.available2021-10-27T20:30:05Z
dc.date.issued2020
dc.identifier.urihttps://hdl.handle.net/1721.1/135948
dc.description.abstract© 2020 John Wiley & Sons, Ltd. Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension instead of exponential scaling. In this paper, we investigate even lower storage-cost representations in the tensor ring format, which is an extension of the tensor train format with variable end-ranks. Firstly, we introduce two algorithms for converting a tensor in full format to tensor ring format with low storage cost. Secondly, we detail a rounding operation for tensor rings and show how this requires new definitions of common linear algebra operations in the format to obtain storage-cost savings. Lastly, we introduce algorithms for transforming the graph structure of graph-based tensor formats, with orders of magnitude lower complexity than existing literature. The efficiency of all algorithms is demonstrated on a number of numerical examples, and in certain cases, we demonstrate significantly higher compression ratios when compared to previous approaches to using the tensor ring format.
dc.language.isoen
dc.publisherWiley
dc.relation.isversionof10.1002/NLA.2289
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.sourcearXiv
dc.titleOn algorithms for and computing with the tensor ring decomposition
dc.typeArticle
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
dc.relation.journalNumerical Linear Algebra with Applications
dc.eprint.versionAuthor's final manuscript
dc.type.urihttp://purl.org/eprint/type/JournalArticle
eprint.statushttp://purl.org/eprint/status/PeerReviewed
dc.date.updated2021-04-30T17:43:49Z
dspace.orderedauthorsMickelin, O; Karaman, S
dspace.date.submission2021-04-30T17:43:50Z
mit.journal.volume27
mit.journal.issue3
mit.licenseOPEN_ACCESS_POLICY
mit.metadata.statusAuthority Work and Publication Information Needed


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