{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:B6L2WRTO6K5TZL3UAH7XH2RGG5","short_pith_number":"pith:B6L2WRTO","schema_version":"1.0","canonical_sha256":"0f97ab466ef2bb3caf7401ff73ea2637602d81b214b6ea59700ae0427196cf35","source":{"kind":"arxiv","id":"1807.04251","version":1},"attestation_state":"computed","paper":{"title":"A study of Schr\\\"oder's method for the matrix $p$th root using power series expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chun-Hua Guo, Di Lu","submitted_at":"2018-07-11T17:14:46Z","abstract_excerpt":"When $A$ is a matrix with all eigenvalues in the disk $|z-1|<1$, the principal $p$th root of $A$ can be computed by Schr\\\"oder's method, among many other methods. In this paper we present a further study of Schr\\\"oder's method for the matrix $p$th root, through an examination of power series expansions of some sequences of scalar functions. Specifically, we obtain a new and informative error estimate for the matrix sequence generated by the Schr\\\"oder's method, a monotonic convergence result when $A$ is a nonsingular $M$-matrix, and a structure preserving result when $A$ is a nonsingular $M$-m"},"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":"1807.04251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-11T17:14:46Z","cross_cats_sorted":[],"title_canon_sha256":"0083a91fa0c8182c06bc60fa5109ae977f9d023be4fffd250f0930e9fe985c4c","abstract_canon_sha256":"9b45c807ab26648a95496e11f10912181e6447cf6ace0328cd8f51e38b5feb25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:57.533102Z","signature_b64":"AyEJWiDgUOYyYN2uFYisHrmAezQNdLyCi9SGI+ctgY5C+hskPOjkVdjlZtAdSRHu+ADC5gTmOC5P7xBfQ6J3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f97ab466ef2bb3caf7401ff73ea2637602d81b214b6ea59700ae0427196cf35","last_reissued_at":"2026-05-18T00:10:57.532428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:57.532428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A study of Schr\\\"oder's method for the matrix $p$th root using power series expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chun-Hua Guo, Di Lu","submitted_at":"2018-07-11T17:14:46Z","abstract_excerpt":"When $A$ is a matrix with all eigenvalues in the disk $|z-1|<1$, the principal $p$th root of $A$ can be computed by Schr\\\"oder's method, among many other methods. In this paper we present a further study of Schr\\\"oder's method for the matrix $p$th root, through an examination of power series expansions of some sequences of scalar functions. Specifically, we obtain a new and informative error estimate for the matrix sequence generated by the Schr\\\"oder's method, a monotonic convergence result when $A$ is a nonsingular $M$-matrix, and a structure preserving result when $A$ is a nonsingular $M$-m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04251","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":"1807.04251","created_at":"2026-05-18T00:10:57.532542+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.04251v1","created_at":"2026-05-18T00:10:57.532542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04251","created_at":"2026-05-18T00:10:57.532542+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6L2WRTO6K5T","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6L2WRTO6K5TZL3U","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6L2WRTO","created_at":"2026-05-18T12:32:13.499390+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/B6L2WRTO6K5TZL3UAH7XH2RGG5","json":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5.json","graph_json":"https://pith.science/api/pith-number/B6L2WRTO6K5TZL3UAH7XH2RGG5/graph.json","events_json":"https://pith.science/api/pith-number/B6L2WRTO6K5TZL3UAH7XH2RGG5/events.json","paper":"https://pith.science/paper/B6L2WRTO"},"agent_actions":{"view_html":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5","download_json":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5.json","view_paper":"https://pith.science/paper/B6L2WRTO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.04251&json=true","fetch_graph":"https://pith.science/api/pith-number/B6L2WRTO6K5TZL3UAH7XH2RGG5/graph.json","fetch_events":"https://pith.science/api/pith-number/B6L2WRTO6K5TZL3UAH7XH2RGG5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5/action/storage_attestation","attest_author":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5/action/author_attestation","sign_citation":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5/action/citation_signature","submit_replication":"https://pith.science/pith/B6L2WRTO6K5TZL3UAH7XH2RGG5/action/replication_record"}},"created_at":"2026-05-18T00:10:57.532542+00:00","updated_at":"2026-05-18T00:10:57.532542+00:00"}