{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VDVDX7PDDB2NGCQ7RPAXOQUD76","short_pith_number":"pith:VDVDX7PD","schema_version":"1.0","canonical_sha256":"a8ea3bfde31874d30a1f8bc1774283ffa198aa65466b876ee13c2408b7191e57","source":{"kind":"arxiv","id":"1611.07239","version":2},"attestation_state":"computed","paper":{"title":"Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bj\\\"orn Sprungk, Lorenzo Tamellini, Oliver G. Ernst","submitted_at":"2016-11-22T10:35:57Z","abstract_excerpt":"We give a convergence proof for the approximation by sparse collocation of Hilbert-space-valued functions depending on countably many Gaussian random variables. Such functions appear as solutions of elliptic PDEs with lognormal diffusion coefficients. We outline a general $L^2$-convergence theory based on previous work by Bachmayr et al. (2016) and Chen (2016) and establish an algebraic convergence rate for sufficiently smooth functions assuming a mild growth bound for the univariate hierarchical surpluses of the interpolation scheme applied to Hermite polynomials. We verify specifically for G"},"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":"1611.07239","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-22T10:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"004e116d6d0f97ad5fba22e6b96cd07887673a88cd8cc130febbd37a00b0f15b","abstract_canon_sha256":"43476b1bad6c914b977023aa406f1f0434d9b0efa97e83197db0f64fe1737752"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:49.269442Z","signature_b64":"T/6b9FoOdm56SAU7tbeksKkFHLA74u3wKKPbwHXYb/TXa+wv/Xcn5iWo4/bTUGbUCcOOBhMUpXBpnOj88XkfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8ea3bfde31874d30a1f8bc1774283ffa198aa65466b876ee13c2408b7191e57","last_reissued_at":"2026-05-18T00:47:49.268895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:49.268895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bj\\\"orn Sprungk, Lorenzo Tamellini, Oliver G. Ernst","submitted_at":"2016-11-22T10:35:57Z","abstract_excerpt":"We give a convergence proof for the approximation by sparse collocation of Hilbert-space-valued functions depending on countably many Gaussian random variables. Such functions appear as solutions of elliptic PDEs with lognormal diffusion coefficients. We outline a general $L^2$-convergence theory based on previous work by Bachmayr et al. (2016) and Chen (2016) and establish an algebraic convergence rate for sufficiently smooth functions assuming a mild growth bound for the univariate hierarchical surpluses of the interpolation scheme applied to Hermite polynomials. We verify specifically for G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07239","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":"1611.07239","created_at":"2026-05-18T00:47:49.268983+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07239v2","created_at":"2026-05-18T00:47:49.268983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07239","created_at":"2026-05-18T00:47:49.268983+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDVDX7PDDB2N","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDVDX7PDDB2NGCQ7","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDVDX7PD","created_at":"2026-05-18T12:30:48.956258+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/VDVDX7PDDB2NGCQ7RPAXOQUD76","json":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76.json","graph_json":"https://pith.science/api/pith-number/VDVDX7PDDB2NGCQ7RPAXOQUD76/graph.json","events_json":"https://pith.science/api/pith-number/VDVDX7PDDB2NGCQ7RPAXOQUD76/events.json","paper":"https://pith.science/paper/VDVDX7PD"},"agent_actions":{"view_html":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76","download_json":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76.json","view_paper":"https://pith.science/paper/VDVDX7PD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07239&json=true","fetch_graph":"https://pith.science/api/pith-number/VDVDX7PDDB2NGCQ7RPAXOQUD76/graph.json","fetch_events":"https://pith.science/api/pith-number/VDVDX7PDDB2NGCQ7RPAXOQUD76/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76/action/storage_attestation","attest_author":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76/action/author_attestation","sign_citation":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76/action/citation_signature","submit_replication":"https://pith.science/pith/VDVDX7PDDB2NGCQ7RPAXOQUD76/action/replication_record"}},"created_at":"2026-05-18T00:47:49.268983+00:00","updated_at":"2026-05-18T00:47:49.268983+00:00"}