{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HS6KCAZ5INYY2NVPIX5ZXFOZHG","short_pith_number":"pith:HS6KCAZ5","schema_version":"1.0","canonical_sha256":"3cbca1033d43718d36af45fb9b95d939bb74ef79844e02990e38fa0559089160","source":{"kind":"arxiv","id":"1703.06155","version":1},"attestation_state":"computed","paper":{"title":"Accuracy Directly Controlled Fast Direct Solutions of General ${\\cal H}^2$-Matrices and Its Application to Electrically Large Integral-Equation-Based Electromagnetic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dan Jiao, Miaomiao Ma","submitted_at":"2017-03-17T18:34:30Z","abstract_excerpt":"The dense matrix resulting from an integral equation (IE) based solution of Maxwell's equations can be compactly represented by an ${\\cal H}^2$-matrix. Given a general dense ${\\cal H}^2$-matrix, prevailing fast direct solutions involve approximations whose accuracy can only be indirectly controlled. In this work, we propose new accuracy-controlled direct solution algorithms, including both factorization and inversion, for solving general ${\\cal H}^2$-matrices, which does not exist prior to this work. Different from existing direct solutions, where the cluster bases are kept unchanged in the so"},"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":"1703.06155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-17T18:34:30Z","cross_cats_sorted":[],"title_canon_sha256":"0f37af92f419c457ea9b2450d62437664cefc0a1baee8bcc9abb48423de5c69d","abstract_canon_sha256":"6dfb717ebb8108a7339bf1258f7a16256f6ffcc4de79f73fc6951f6d92493b16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:34.554662Z","signature_b64":"ZxnU9uSdz7Vg+K2Wzgz6orTR/iAANBxHDTFAU7FPpuUz8Z7skBUQL/P9KRAfy3ruGbkozzSS9QR4AK1I7trkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cbca1033d43718d36af45fb9b95d939bb74ef79844e02990e38fa0559089160","last_reissued_at":"2026-05-18T00:25:34.553920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:34.553920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Accuracy Directly Controlled Fast Direct Solutions of General ${\\cal H}^2$-Matrices and Its Application to Electrically Large Integral-Equation-Based Electromagnetic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dan Jiao, Miaomiao Ma","submitted_at":"2017-03-17T18:34:30Z","abstract_excerpt":"The dense matrix resulting from an integral equation (IE) based solution of Maxwell's equations can be compactly represented by an ${\\cal H}^2$-matrix. Given a general dense ${\\cal H}^2$-matrix, prevailing fast direct solutions involve approximations whose accuracy can only be indirectly controlled. In this work, we propose new accuracy-controlled direct solution algorithms, including both factorization and inversion, for solving general ${\\cal H}^2$-matrices, which does not exist prior to this work. Different from existing direct solutions, where the cluster bases are kept unchanged in the so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06155","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":"1703.06155","created_at":"2026-05-18T00:25:34.554026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06155v1","created_at":"2026-05-18T00:25:34.554026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06155","created_at":"2026-05-18T00:25:34.554026+00:00"},{"alias_kind":"pith_short_12","alias_value":"HS6KCAZ5INYY","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HS6KCAZ5INYY2NVP","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HS6KCAZ5","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG","json":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG.json","graph_json":"https://pith.science/api/pith-number/HS6KCAZ5INYY2NVPIX5ZXFOZHG/graph.json","events_json":"https://pith.science/api/pith-number/HS6KCAZ5INYY2NVPIX5ZXFOZHG/events.json","paper":"https://pith.science/paper/HS6KCAZ5"},"agent_actions":{"view_html":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG","download_json":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG.json","view_paper":"https://pith.science/paper/HS6KCAZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06155&json=true","fetch_graph":"https://pith.science/api/pith-number/HS6KCAZ5INYY2NVPIX5ZXFOZHG/graph.json","fetch_events":"https://pith.science/api/pith-number/HS6KCAZ5INYY2NVPIX5ZXFOZHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG/action/storage_attestation","attest_author":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG/action/author_attestation","sign_citation":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG/action/citation_signature","submit_replication":"https://pith.science/pith/HS6KCAZ5INYY2NVPIX5ZXFOZHG/action/replication_record"}},"created_at":"2026-05-18T00:25:34.554026+00:00","updated_at":"2026-05-18T00:25:34.554026+00:00"}