{"id":"https://openalex.org/W7158130027","doi":"https://doi.org/10.48550/arxiv.2604.25411","title":"Convergence analysis of a full discretization of operator-valued differential Riccati equations","display_name":"Convergence analysis of a full discretization of operator-valued differential Riccati equations","publication_year":2026,"publication_date":"2026-04-28","ids":{"openalex":"https://openalex.org/W7158130027","doi":"https://doi.org/10.48550/arxiv.2604.25411"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.25411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.25411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.25411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102773573","display_name":"Eskil Hansen","orcid":"https://orcid.org/0000-0003-1187-6967"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hansen, Eskil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043010366","display_name":"Tony Stillfjord","orcid":"https://orcid.org/0000-0001-6123-4271"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stillfjord, Tony","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134857295","display_name":"Teodor \u00c5berg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u00c5berg, Teodor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.16949999332427979,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.16949999332427979,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.09109999984502792,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.08150000125169754,"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/discretization","display_name":"Discretization","score":0.8596000075340271},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6987000107765198},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5404000282287598},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.48170000314712524},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.45500001311302185},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43630000948905945},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.40310001373291016},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.3903999924659729},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.3856000006198883}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8596000075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.774399995803833},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6987000107765198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5813999772071838},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5404000282287598},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.48170000314712524},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.45500001311302185},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43630000948905945},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37950000166893005},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C105427703","wikidata":"https://www.wikidata.org/wiki/Q665193","display_name":"Discretization of continuous features","level":4,"score":0.3659000098705292},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3231000006198883},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3163999915122986},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.3109000027179718},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C2778327290","wikidata":"https://www.wikidata.org/wiki/Q17146496","display_name":"Temporal discretization","level":3,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.25411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.25411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.25411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.25411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.5235324501991272,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,32],"recent":[1],"previous":[2],"work":[3],"[E.":[4],"Hansen,":[5],"T.":[6,9],"Stillfjord":[7],"and":[8,53,83,132],"\u00c5berg,":[10],"SIAM":[11],"J.":[12],"Numer.":[13],"Anal.,":[14],"to":[15,26,98],"appear],":[16],"we":[17,35,61],"analyzed":[18],"the":[19,41,66,101,124,142],"convergence":[20,42],"of":[21,43,77,80,85],"operator":[22],"splitting":[23,55],"methods":[24],"applied":[25],"operator-valued":[27],"differential":[28],"Riccati":[29],"equations":[30],"(DRE).":[31],"this":[33,64,106],"paper,":[34],"extend":[36],"these":[37],"results":[38],"by":[39,148],"analyzing":[40],"a":[44,149],"full":[45,102],"discretization":[46,103],"based":[47,152],"on":[48,141,153],"finite":[49],"elements":[50],"in":[51,56,112,130,135,156],"space":[52],"Lie":[54],"time.":[57],"As":[58],"far":[59],"as":[60],"are":[62,73],"aware,":[63],"is":[65,95,107,118,146],"first":[67],"such":[68],"analysis":[69],"for":[70,121],"DRE.":[71],"There":[72],"very":[74],"few":[75],"analyses":[76],"temporal":[78],"discretizations":[79],"DRE":[81],"overall,":[82],"none":[84],"them":[86],"have":[87],"been":[88],"combined":[89],"with":[90,127],"spatial":[91],"discretizations.":[92],"However,":[93],"it":[94],"clearly":[96],"vital":[97],"know":[99],"when":[100],"converges,":[104],"since":[105],"what":[108],"will":[109],"be":[110],"used":[111],"practical":[113],"applications.":[114],"Our":[115],"main":[116],"result":[117],"that":[119],"except":[120],"logarithmic":[122],"factors,":[123],"method":[125],"converges":[126],"order":[128,133],"one":[129],"time":[131],"two":[134],"space,":[136],"under":[137],"fairly":[138],"weak":[139],"assumptions":[140],"problem":[143],"data.":[144],"This":[145],"illustrated":[147],"numerical":[150],"experiment":[151],"an":[154],"application":[155],"optimal":[157],"control.":[158]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-30T00:00:00"}