{"id":"https://openalex.org/W2038417508","doi":"https://doi.org/10.1137/s0036142900374482","title":"Convergence of Optimal Prediction for Nonlinear Hamiltonian Systems","display_name":"Convergence of Optimal Prediction for Nonlinear Hamiltonian Systems","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2038417508","doi":"https://doi.org/10.1137/s0036142900374482","mag":"2038417508"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900374482","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900374482","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021208510","display_name":"Ole H. Hald","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ole H. Hald","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019609183","display_name":"Raz Kupferman","orcid":"https://orcid.org/0000-0001-7699-7466"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Raz Kupferman","raw_affiliation_strings":["Hebrew University of Jerusalem ,"],"affiliations":[{"raw_affiliation_string":"Hebrew University of Jerusalem ,","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021208510"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0494,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7786176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"39","issue":"3","first_page":"983","last_page":"1000"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7764186859130859},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.6619200706481934},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6348177194595337},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6124667525291443},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5807821154594421},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.47195592522621155},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4612864553928375},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3948317766189575},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07903614640235901}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7764186859130859},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.6619200706481934},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6348177194595337},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6124667525291443},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5807821154594421},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.47195592522621155},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4612864553928375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3948317766189575},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07903614640235901},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142900374482","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900374482","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1480995589","https://openalex.org/W1641427243","https://openalex.org/W1708785370","https://openalex.org/W1968716084","https://openalex.org/W1969190169","https://openalex.org/W1981911537","https://openalex.org/W2009295400","https://openalex.org/W2012872617","https://openalex.org/W2023743841","https://openalex.org/W2080705033","https://openalex.org/W2160695687","https://openalex.org/W2164193727","https://openalex.org/W2171367752","https://openalex.org/W3103102496"],"related_works":["https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W138907054","https://openalex.org/W2536422707","https://openalex.org/W24145419","https://openalex.org/W2044869171","https://openalex.org/W1590887574"],"abstract_inverted_index":{"Optimal":[0],"prediction":[1,30,61,78],"is":[2,74,79],"a":[3,25,32,43],"computational":[4],"method":[5],"for":[6,42,54],"systems":[7],"that":[8,76,82],"cannot":[9],"be":[10],"properly":[11],"resolved,":[12],"in":[13],"which":[14],"the":[15,37,40,55,59,64,80,84],"unresolved":[16],"variables":[17],"are":[18],"viewed":[19],"as":[20,31],"random.":[21],"This":[22],"paper":[23],"presents":[24],"first":[26],"analysis":[27],"of":[28,39,45,47,66],"optimal":[29,60,77],"numerical":[33],"method.":[34],"We":[35],"prove":[36],"convergence":[38],"scheme":[41,81],"class":[44],"equations":[46],"Schr\u00f6dinger":[48],"type":[49],"and":[50,63],"derive":[51],"error":[52,57],"bounds":[53],"mean":[56,85],"between":[58],"solution":[62],"set":[65],"exact":[67],"solutions":[68],"with":[69],"random":[70],"initial":[71],"data.":[72],"It":[73],"shown":[75],"minimizes":[83],"truncation":[86],"error.":[87]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
