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The algorithm runs in time\n  $$\\tilde{O}((m \\log{n} + n\\log^2{n})\\log(1/p)).$$\n  As a result, we obtain an algorithm that on input of an $n\\times n$ symmetric diagonally dominant matrix $A$ with $m$ non-zero entries and a vector $b$, computes a vector ${x}$ satisfying $||{x}-A^{+}b||_A<\\epsilon ||A^{+}b"},"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":"1003.2958","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-03-15T16:37:51Z","cross_cats_sorted":[],"title_canon_sha256":"498a615e3c197d5d5957de1a8e8468e2d4cbe8655aede1a301ee0f6d565cf63b","abstract_canon_sha256":"d3a070cdf5716cc7c7181b1296f9edda80f8f5660d07637ee059827173dfdb6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:37.124946Z","signature_b64":"os+F2DI9IkVH608un2vpBgmWZQUr6jazrHF9FQqpU2pPpexAH2fwXCne/PWLEzuKTAMM3h1o7Bk4qMFXcaJfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a20a3c9454a1ae90096c37af5475c3c561175fd3ca846e51bbe3a3fc14d185b4","last_reissued_at":"2026-05-18T02:24:37.124236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:37.124236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approaching optimality for solving SDD systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Gary L. 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