{"id":"https://openalex.org/W2789735464","doi":"https://doi.org/10.1109/tac.2018.2798703","title":"Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple","display_name":"Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple","publication_year":2018,"publication_date":"2018-01-26","ids":{"openalex":"https://openalex.org/W2789735464","doi":"https://doi.org/10.1109/tac.2018.2798703","mag":"2789735464"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2798703","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2798703","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5018011442","display_name":"Goran Marjanovic","orcid":"https://orcid.org/0000-0003-2016-2384"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Goran Marjanovic","raw_affiliation_strings":["School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091154507","display_name":"Victor Solo","orcid":"https://orcid.org/0000-0002-5123-7708"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Victor Solo","raw_affiliation_strings":["School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018011442"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":3.1367,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.90201514,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"63","issue":"12","first_page":"4035","last_page":"4050"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.6352270841598511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6032214760780334},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5595142841339111},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5358741283416748},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5066152811050415},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4492458701133728},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.4419940412044525},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4180223345756531},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4121084213256836},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3427474796772003},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2223210334777832},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15952521562576294}],"concepts":[{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.6352270841598511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6032214760780334},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5595142841339111},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5358741283416748},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5066152811050415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4492458701133728},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.4419940412044525},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4180223345756531},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4121084213256836},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3427474796772003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2223210334777832},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15952521562576294},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2018.2798703","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2798703","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W161929197","https://openalex.org/W578359435","https://openalex.org/W1489270186","https://openalex.org/W1544770838","https://openalex.org/W1551148884","https://openalex.org/W1561367079","https://openalex.org/W1892810859","https://openalex.org/W1969080261","https://openalex.org/W1969164173","https://openalex.org/W1983958833","https://openalex.org/W1992278142","https://openalex.org/W1994384777","https://openalex.org/W2016012557","https://openalex.org/W2035008549","https://openalex.org/W2040643815","https://openalex.org/W2044640615","https://openalex.org/W2045308959","https://openalex.org/W2049046732","https://openalex.org/W2055843842","https://openalex.org/W2061356302","https://openalex.org/W2088449330","https://openalex.org/W2094210680","https://openalex.org/W2096487710","https://openalex.org/W2103160683","https://openalex.org/W2131838761","https://openalex.org/W2131889108","https://openalex.org/W2132240870","https://openalex.org/W2140393629","https://openalex.org/W2140710100","https://openalex.org/W2144707556","https://openalex.org/W2145137020","https://openalex.org/W2151249889","https://openalex.org/W2168278516","https://openalex.org/W2170316986","https://openalex.org/W2224043109","https://openalex.org/W2292394767","https://openalex.org/W2408175243","https://openalex.org/W2515882314","https://openalex.org/W2546505240","https://openalex.org/W2569171899","https://openalex.org/W2573293482","https://openalex.org/W2915178317","https://openalex.org/W4205510932","https://openalex.org/W4211165101","https://openalex.org/W4231021340","https://openalex.org/W4243961535","https://openalex.org/W4285719527","https://openalex.org/W4300900232","https://openalex.org/W6606617128","https://openalex.org/W6665717006","https://openalex.org/W6675620244","https://openalex.org/W6684910095"],"related_works":["https://openalex.org/W620239920","https://openalex.org/W109055908","https://openalex.org/W1546584948","https://openalex.org/W2060658157","https://openalex.org/W2972896374","https://openalex.org/W2164842548","https://openalex.org/W4237379163","https://openalex.org/W2085400897","https://openalex.org/W3150981116","https://openalex.org/W3136773326"],"abstract_inverted_index":{"A":[0],"large":[1],"number":[2],"of":[3,9,28,74],"significant":[4],"applications":[5],"involve":[6],"numerical":[7,29,75,103],"solution":[8,46],"stochastic":[10],"differential":[11,85],"equations":[12],"(SDE's)":[13],"evolving":[14],"in":[15,48,66],"Lie":[16,50],"groups":[17],"such":[18],"as":[19],"SO(3).":[20],"In":[21,92],"the":[22,25,45,49,102],"engineering":[23],"literature,":[24],"proper":[26],"formulation":[27],"schemes":[30,38,76,104],"has":[31],"largely":[32],"been":[33],"ignored":[34],"so":[35],"that":[36,80],"many":[37],"are":[39],"flawed,":[40],"i.e.,":[41],"do":[42,81],"not":[43,61,82],"guarantee":[44],"stays":[47],"group.":[51],"There":[52],"is":[53,60],"a":[54,70],"small":[55],"mathematics":[56],"literature":[57],"but":[58],"it":[59],"easily":[62],"accessible.":[63],"With":[64],"this":[65],"mind,":[67],"we":[68,95],"give":[69],"directly":[71],"accessible":[72],"derivation":[73],"for":[77],"solving":[78],"SDE's":[79],"rely":[83],"on":[84],"geometry":[86],"or":[87],"advanced":[88],"random":[89],"process":[90],"theory.":[91],"doing":[93],"so,":[94],"develop":[96],"some":[97],"new":[98],"results.":[99],"We":[100],"illustrate":[101],"with":[105],"simulations.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}