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We complement this result by an analysis of approximate multipoint evaluation of $F$ to a precision of $L$ bits after the binary point and prove a bit complexity of $\\tilde{O}(n(L + \\tau + n\\Gamma)),$ where $2^\\tau$ and $2^\\Gamma,$ with $\\tau, \\Gamma \\in \\mathbb{N}_{\\ge 1},$ ar"},"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":"1304.8069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-04-30T17:01:11Z","cross_cats_sorted":["cs.SC","math.NA"],"title_canon_sha256":"c7305079bdae465bad3484c89480a2b21d9db45e9345d82853d07b069ec22287","abstract_canon_sha256":"67a9901defd29de5f046802945055f8239f29bfed650d5dee6edab761505cf8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:31.324397Z","signature_b64":"YaxElLy+amLtT86ZYPYxjyYULY1+nHtoe4eWoyvAUXSxTD4Chi7+ABWdkxZVaoSAQfpVjsQRqnpfc0VNOEnlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d7e06538038cbb8eac82a87078f16c44233d3a46d3a0b4738db2ba597457dd1","last_reissued_at":"2026-05-18T01:13:31.323648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:31.323648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Approximate Polynomial Multipoint Evaluation and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NA"],"primary_cat":"cs.NA","authors_text":"Alexander Kobel, Michael Sagraloff","submitted_at":"2013-04-30T17:01:11Z","abstract_excerpt":"It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \\in \\mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\\tilde{O}(n)$ exact field operations in $\\mathbb{C},$ where $\\tilde{O}(\\cdot)$ means that we omit polylogarithmic factors. 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