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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.0417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-02T11:19:11Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"2da2a849c0ce61e8c3e1b9cbb8e4195b8cdadcdb0fd4dcea27dd73f69770decb","abstract_canon_sha256":"8bff0737ef0ee8792f5e9c7522dabf93433c12afb10aa5770c0bebd9739cb5c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:58.631375Z","signature_b64":"IXN6YgjGIS0g0yGkaMsZ5tYEMImkVaVLP2FoCK3tow7uO0MXCk8zdFFhf5MxkzicyvWnPQp+0RlsRl/8/EAYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ed9ad9cc11427eccd146ec5d4bbd8faa31f2af05ff7e076d5ac79e9ba219bfc","last_reissued_at":"2026-05-18T02:50:58.630734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:58.630734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\matA$. 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