{"paper":{"title":"Faster SVD-Truncated Least-Squares Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.DS","authors_text":"Christos Boutsidis, Malik Magdon-Ismail","submitted_at":"2014-01-02T11:19:11Z","abstract_excerpt":"We develop a fast algorithm for computing the \"SVD-truncated\" regularized solution to the least-squares problem: $ \\min_{\\x} \\TNorm{\\matA \\x - \\b}. $ Let $\\matA_k$ of rank $k$ be the best rank $k$ matrix computed via the SVD of $\\matA$. Then, the SVD-truncated regularized solution is: $ \\x_k = \\pinv{\\matA}_k \\b. $ If $\\matA$ is $m \\times n$, then, it takes $O(m n \\min\\{m,n\\})$ time to compute $\\x_k $ using the SVD of \\math{\\matA}. We give an approximation algorithm for \\math{\\x_k} which constructs a rank-\\math{k} approximation $\\tilde{\\matA}_{k}$ and computes $ \\tilde{\\x}_{k} = \\pinv{\\tilde\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0417","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"}