{"corpus_id":121754764,"paper_sha":"29f2773a5906a4306fb5e8b7104a309bff2b462e","doi":"10.1016/S0377-0427(97)00036-8","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2009835983,"dblp_id":null,"acl_id":null,"title":"On the convergence of parallel chaotic nonlinear multisplitting Newton-type methods","year":1997,"publication_date":"1997-05-05","venue":"","journal":{"name":"Journal of Computational and Applied Mathematics","pages":"317-334","volume":"80"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Computer Science"],"reference_count":11,"citation_count":16,"influential_citation_count":0,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract A class of parallel chaotic nonlinear multisplitting Newton-type methods for solving the nonlinear system of equations F ( x ) = 0( F : D ⊂ R n → R n ) is established and its local convergence theory is presented.","claims":[{"public_id":"cl_e36e10eeb5a280dc679568a0ea4004f9","status":"active","text":"A class of parallel chaotic nonlinear multisplitting Newton-type methods is established for solving nonlinear systems of equations F(x)=0.","confidence":0.95,"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/claims/cl_e36e10eeb5a280dc679568a0ea4004f9"},{"public_id":"cl_21d74af97173fc5acf098aa3406eaeb3","status":"active","text":"Local convergence theory is presented for the established parallel chaotic nonlinear multisplitting Newton-type methods.","confidence":0.92,"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/claims/cl_21d74af97173fc5acf098aa3406eaeb3"}],"concepts":[{"public_id":"co_2b8d863c671acda957249383f10ef215","status":"active","name":"parallel chaotic nonlinear multisplitting Newton-type methods","description":"A class of iterative Newton-type algorithms with parallel, chaotic, and nonlinear multisplitting features for nonlinear equations.","types":["method"],"aliases":[],"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/concepts/co_2b8d863c671acda957249383f10ef215"},{"public_id":"co_327b8dbd1fb5c57039781166cd41e4d8","status":"active","name":"local convergence theory","description":"A theoretical framework describing convergence behavior near a solution of the nonlinear system.","types":["theoretical framework"],"aliases":[],"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/concepts/co_327b8dbd1fb5c57039781166cd41e4d8"},{"public_id":"co_bb271e01ce0764d3820a722e5f25b385","status":"active","name":"Newton-type methods","description":"Iterative numerical methods related to Newton's method for solving equations.","types":["method family"],"aliases":[],"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/concepts/co_bb271e01ce0764d3820a722e5f25b385"},{"public_id":"co_bdca5dd6c6e1b64b0cc40f0bcc997c86","status":"active","name":"nonlinear system of equations F(x)=0","description":"The nonlinear equation-solving problem where a vector-valued function F is set equal to zero.","types":["problem"],"aliases":["F(x)=0"],"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/concepts/co_bdca5dd6c6e1b64b0cc40f0bcc997c86"},{"public_id":"co_d84e401482b204d7f14e7dfc138d1c40","status":"active","name":"nonlinear multisplitting","description":"A splitting-based approach for nonlinear systems that divides the computation into multiple components.","types":["method component"],"aliases":[],"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/concepts/co_d84e401482b204d7f14e7dfc138d1c40"},{"public_id":"co_de9ee854c898d6355d324212b057b7d9","status":"active","name":"parallel chaotic","description":"A computational mode in which parallel iterative updates may proceed in an asynchronous or unordered fashion.","types":["computational strategy"],"aliases":[],"contributors":[{"id":35,"public_id":"b2adb6bfad","public_label":"Anonymous (b2adb6bfad)","roles":["extraction"],"url":"https://sah.borca.ai/u/b2adb6bfad"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/concepts/co_de9ee854c898d6355d324212b057b7d9"}],"external_ids":{"DOI":"10.1016/S0377-0427(97)00036-8","ArXiv":null,"PubMed":null,"PubMedCentral":null,"MAG":2009835983,"DBLP":null,"ACL":null},"open_access":{"is_open_access":false,"pdf_url":null,"landing_url":"https://sah.borca.ai/papers/121754764","source":null,"pdf_url_source":null,"license":null,"reason":"pdf_url_not_indexed"},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":false,"full_text_source":null,"count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":630799,"paper_uid":"3fa85d5c-b5b7-4394-83fc-ab41ca6b7de0","canonical_identity":{"paper_id":630799,"paper_uid":"3fa85d5c-b5b7-4394-83fc-ab41ca6b7de0","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/121754764"}