{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VPFZREW3WIWAZN2DRTNBAK3QK6","short_pith_number":"pith:VPFZREW3","schema_version":"1.0","canonical_sha256":"abcb9892dbb22c0cb7438cda102b705790b1effde7515348edd2392c0944a3b4","source":{"kind":"arxiv","id":"1304.7796","version":2},"attestation_state":"computed","paper":{"title":"Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"2) ((1) IGPM, (2) AICES, Markus Bachmayr (1), RWTH Aachen, RWTH Aachen), Wolfgang Dahmen (1","submitted_at":"2013-04-29T20:34:05Z","abstract_excerpt":"We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous convergence analysis, where all parameters required for the execution of the methods depend only on the underlying infinite-dimensional problem, but not on a concrete discretization. Under certain assumptions on the rates for the involved low-rank approximations and basis expansions, we can also give bounds on the computational complexity of the iteration as a "},"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":"1304.7796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-29T20:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"0f37598f0952ddf90dc861cf76c567db232da913ddb73d60fcee85f5b664441d","abstract_canon_sha256":"9e2ff8d12c69ea8a70b83c46b20bccc80802f290641a95b5321e3d743fa543e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:21.303117Z","signature_b64":"wbLVkG1qdFfq34HCSdkle28c6cgyJw9np0hj0FReZUer6Jifyr1Yb8FhhrydC9tH9ISd4TuK3gQEN8op4Nf4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abcb9892dbb22c0cb7438cda102b705790b1effde7515348edd2392c0944a3b4","last_reissued_at":"2026-05-18T02:56:21.302531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:21.302531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"2) ((1) IGPM, (2) AICES, Markus Bachmayr (1), RWTH Aachen, RWTH Aachen), Wolfgang Dahmen (1","submitted_at":"2013-04-29T20:34:05Z","abstract_excerpt":"We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous convergence analysis, where all parameters required for the execution of the methods depend only on the underlying infinite-dimensional problem, but not on a concrete discretization. Under certain assumptions on the rates for the involved low-rank approximations and basis expansions, we can also give bounds on the computational complexity of the iteration as a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7796","kind":"arxiv","version":2},"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":"1304.7796","created_at":"2026-05-18T02:56:21.302628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7796v2","created_at":"2026-05-18T02:56:21.302628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7796","created_at":"2026-05-18T02:56:21.302628+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPFZREW3WIWA","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPFZREW3WIWAZN2D","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPFZREW3","created_at":"2026-05-18T12:28:04.890932+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/VPFZREW3WIWAZN2DRTNBAK3QK6","json":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6.json","graph_json":"https://pith.science/api/pith-number/VPFZREW3WIWAZN2DRTNBAK3QK6/graph.json","events_json":"https://pith.science/api/pith-number/VPFZREW3WIWAZN2DRTNBAK3QK6/events.json","paper":"https://pith.science/paper/VPFZREW3"},"agent_actions":{"view_html":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6","download_json":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6.json","view_paper":"https://pith.science/paper/VPFZREW3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7796&json=true","fetch_graph":"https://pith.science/api/pith-number/VPFZREW3WIWAZN2DRTNBAK3QK6/graph.json","fetch_events":"https://pith.science/api/pith-number/VPFZREW3WIWAZN2DRTNBAK3QK6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6/action/storage_attestation","attest_author":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6/action/author_attestation","sign_citation":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6/action/citation_signature","submit_replication":"https://pith.science/pith/VPFZREW3WIWAZN2DRTNBAK3QK6/action/replication_record"}},"created_at":"2026-05-18T02:56:21.302628+00:00","updated_at":"2026-05-18T02:56:21.302628+00:00"}