{"paper":{"title":"LSRN: A Parallel Iterative Solver for Strongly Over- or Under-Determined Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","cs.NA"],"primary_cat":"cs.DS","authors_text":"Michael A. Saunders, Michael W. Mahoney, Xiangrui Meng","submitted_at":"2011-09-27T18:06:44Z","abstract_excerpt":"We describe a parallel iterative least squares solver named \\texttt{LSRN} that is based on random normal projection. \\texttt{LSRN} computes the min-length solution to $\\min_{x \\in \\mathbb{R}^n} \\|A x - b\\|_2$, where $A \\in \\mathbb{R}^{m \\times n}$ with $m \\gg n$ or $m \\ll n$, and where $A$ may be rank-deficient. Tikhonov regularization may also be included. Since $A$ is only involved in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and \\texttt{LSRN} automatically speeds up when $A$ is sparse or a fast linear operator. The precondition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5981","kind":"arxiv","version":2},"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"}