{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5EBIFKXNPKSJWVZT2J7V5ARIXR","short_pith_number":"pith:5EBIFKXN","schema_version":"1.0","canonical_sha256":"e90282aaed7aa49b5733d27f5e8228bc4036a69c0095b41023ef4c359d4298c1","source":{"kind":"arxiv","id":"1509.07919","version":1},"attestation_state":"computed","paper":{"title":"Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","cs.NA"],"primary_cat":"cs.DC","authors_text":"Ang Li, Dan Negrut, Radu Serban","submitted_at":"2015-09-25T23:04:17Z","abstract_excerpt":"We discuss an approach for solving sparse or dense banded linear systems ${\\bf A} {\\bf x} = {\\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\\bf A} \\in {\\mathbb{R}}^{N \\times N}$ is possibly nonsymmetric and moderately large; i.e., $10000 \\leq N \\leq 500000$. The ${\\it split\\ and\\ parallelize}$ (${\\tt SaP}$) approach seeks to partition the matrix ${\\bf A}$ into diagonal sub-blocks ${\\bf A}_i$, $i=1,\\ldots,P$, which are independently factored in parallel. The solution may choose to consider or to ignore the matrices that couple the diagonal sub-blocks ${\\bf A}_i$. This approach, "},"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":"1509.07919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-09-25T23:04:17Z","cross_cats_sorted":["cs.MS","cs.NA"],"title_canon_sha256":"cc5a98b7db87b8f407da86aeb4cd6c8ac10e89b3db472e132fe2c93c2bc7e7b4","abstract_canon_sha256":"e714073a3f3e605991f7efccb9b2ac0191d072d3345f0b2d23b1b2e440a71ac0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:59.733617Z","signature_b64":"TZlZ+bSwz5lWObZXDNZbnuVUD6F/2zzHi8QafDgljFiS51ry3CZGXiXVfGpVNxpo5sjLlDJo3WJ5/oaHAmlrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e90282aaed7aa49b5733d27f5e8228bc4036a69c0095b41023ef4c359d4298c1","last_reissued_at":"2026-05-18T01:31:59.733130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:59.733130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","cs.NA"],"primary_cat":"cs.DC","authors_text":"Ang Li, Dan Negrut, Radu Serban","submitted_at":"2015-09-25T23:04:17Z","abstract_excerpt":"We discuss an approach for solving sparse or dense banded linear systems ${\\bf A} {\\bf x} = {\\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\\bf A} \\in {\\mathbb{R}}^{N \\times N}$ is possibly nonsymmetric and moderately large; i.e., $10000 \\leq N \\leq 500000$. The ${\\it split\\ and\\ parallelize}$ (${\\tt SaP}$) approach seeks to partition the matrix ${\\bf A}$ into diagonal sub-blocks ${\\bf A}_i$, $i=1,\\ldots,P$, which are independently factored in parallel. The solution may choose to consider or to ignore the matrices that couple the diagonal sub-blocks ${\\bf A}_i$. This approach, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07919","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":"1509.07919","created_at":"2026-05-18T01:31:59.733208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07919v1","created_at":"2026-05-18T01:31:59.733208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07919","created_at":"2026-05-18T01:31:59.733208+00:00"},{"alias_kind":"pith_short_12","alias_value":"5EBIFKXNPKSJ","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5EBIFKXNPKSJWVZT","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5EBIFKXN","created_at":"2026-05-18T12:29:05.191682+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/5EBIFKXNPKSJWVZT2J7V5ARIXR","json":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR.json","graph_json":"https://pith.science/api/pith-number/5EBIFKXNPKSJWVZT2J7V5ARIXR/graph.json","events_json":"https://pith.science/api/pith-number/5EBIFKXNPKSJWVZT2J7V5ARIXR/events.json","paper":"https://pith.science/paper/5EBIFKXN"},"agent_actions":{"view_html":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR","download_json":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR.json","view_paper":"https://pith.science/paper/5EBIFKXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07919&json=true","fetch_graph":"https://pith.science/api/pith-number/5EBIFKXNPKSJWVZT2J7V5ARIXR/graph.json","fetch_events":"https://pith.science/api/pith-number/5EBIFKXNPKSJWVZT2J7V5ARIXR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR/action/storage_attestation","attest_author":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR/action/author_attestation","sign_citation":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR/action/citation_signature","submit_replication":"https://pith.science/pith/5EBIFKXNPKSJWVZT2J7V5ARIXR/action/replication_record"}},"created_at":"2026-05-18T01:31:59.733208+00:00","updated_at":"2026-05-18T01:31:59.733208+00:00"}