{"paper":{"title":"Alternating Least Squares Tensor Completion in The TT-Format","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lars Grasedyck, Melanie Kluge, Sebastian Kr\\\"amer","submitted_at":"2015-09-01T14:22:42Z","abstract_excerpt":"We consider the problem of fitting a low rank tensor $A\\in\\mathbb{R}^{{\\mathcal I}}$, ${\\mathcal I} = \\{1,\\ldots,n\\}^{d}$, to a given set of data points $\\{M_i\\in\\mathbb{R}\\mid i\\in P\\}$, $P\\subset{\\mathcal I}$.\n  The low rank format under consideration is the hierarchical or TT or MPS format. It is characterized by rank bounds $r$ on certain matricizations of the tensor. The number of degrees of freedom is in ${\\cal O}(r^2dn)$.\n  For a fixed rank and mode size $n$ we observe that it is possible to reconstruct random (but rank structured) tensors as well as certain discretized multivariate (bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00311","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}