{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:X55ZRAZBS2XK4G2XNNCTVV3KRQ","short_pith_number":"pith:X55ZRAZB","schema_version":"1.0","canonical_sha256":"bf7b98832196aeae1b576b453ad76a8c2c9ac3d0cdca570035da716c99bdd63c","source":{"kind":"arxiv","id":"1407.1572","version":1},"attestation_state":"computed","paper":{"title":"The Inverse Fast Multipole Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Eric Darve, Sivaram Ambikasaran","submitted_at":"2014-07-07T03:16:40Z","abstract_excerpt":"This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \\emph{The highlight of this new fast direct solver is that the solver scales linearly in the number of unknowns in all dimensions.} The solver, termed as Inverse Fast Multipole Method (abbreviated as IFMM), works on the same data-structure as the Fast Multipole Method (abbreviated as FMM). More generally, the solver can be immediately extended to the class of hierarchical matrices, denoted as"},"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":"1407.1572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-07T03:16:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"075d9117f0ece86428b66b581c84e68435443a583745868a1799b68ac9a0fb4a","abstract_canon_sha256":"ecf8a38f303fa41fb06843789b4f8868bd4f0032b83ea4cbcb680ae5057ba80e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:11.026252Z","signature_b64":"ZrAEv6GM6sBg5cmInlZ1Z20TOF+U1T1of4Qugq3+cuRTfhYmbiKpus9c2VcHvodU6RK7gauilhGzOjo2WxD4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf7b98832196aeae1b576b453ad76a8c2c9ac3d0cdca570035da716c99bdd63c","last_reissued_at":"2026-05-18T02:48:11.025559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:11.025559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Inverse Fast Multipole Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Eric Darve, Sivaram Ambikasaran","submitted_at":"2014-07-07T03:16:40Z","abstract_excerpt":"This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \\emph{The highlight of this new fast direct solver is that the solver scales linearly in the number of unknowns in all dimensions.} The solver, termed as Inverse Fast Multipole Method (abbreviated as IFMM), works on the same data-structure as the Fast Multipole Method (abbreviated as FMM). More generally, the solver can be immediately extended to the class of hierarchical matrices, denoted as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1572","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.1572","created_at":"2026-05-18T02:48:11.025690+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1572v1","created_at":"2026-05-18T02:48:11.025690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1572","created_at":"2026-05-18T02:48:11.025690+00:00"},{"alias_kind":"pith_short_12","alias_value":"X55ZRAZBS2XK","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"X55ZRAZBS2XK4G2X","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"X55ZRAZB","created_at":"2026-05-18T12:28:54.890064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2602.14289","citing_title":"Parallel Sparse and Data-Sparse Factorization-based Linear Solvers","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ","json":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ.json","graph_json":"https://pith.science/api/pith-number/X55ZRAZBS2XK4G2XNNCTVV3KRQ/graph.json","events_json":"https://pith.science/api/pith-number/X55ZRAZBS2XK4G2XNNCTVV3KRQ/events.json","paper":"https://pith.science/paper/X55ZRAZB"},"agent_actions":{"view_html":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ","download_json":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ.json","view_paper":"https://pith.science/paper/X55ZRAZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1572&json=true","fetch_graph":"https://pith.science/api/pith-number/X55ZRAZBS2XK4G2XNNCTVV3KRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/X55ZRAZBS2XK4G2XNNCTVV3KRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ/action/storage_attestation","attest_author":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ/action/author_attestation","sign_citation":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ/action/citation_signature","submit_replication":"https://pith.science/pith/X55ZRAZBS2XK4G2XNNCTVV3KRQ/action/replication_record"}},"created_at":"2026-05-18T02:48:11.025690+00:00","updated_at":"2026-05-18T02:48:11.025690+00:00"}