{"paper":{"title":"TT-LSQR For Tensor Least Squares Problems and Application to Data Mining *","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Lorenzo Piccinini, Valeria Simoncini","submitted_at":"2025-02-03T12:12:52Z","abstract_excerpt":"We are interested in the numerical solution of the tensor least squares problem \\[\n  \\min_{\\mathcal{X}} \\| \\mathcal{F} - \\sum_{i =1}^{\\ell} \\mathcal{X} \\times_1 A_1^{(i)} \\times_2 A_2^{(i)} \\cdots \\times_d A_d^{(i)} \\|_F, \\] where $\\mathcal{X}\\in\\mathbb{R}^{m_1 \\times m_2 \\times \\cdots \\times m_d}$, $\\mathcal{F}\\in\\mathbb{R}^{n_1\\times n_2 \\times \\cdots \\times n_d}$ are tensors with $d$ dimensions, and the coefficients $A_j^{(i)}$ are tall matrices of conforming dimensions. We first describe a tensor implementation of the classical LSQR method by Paige and Saunders, using the tensor-train repr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01293","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01293/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}