{"id":"https://openalex.org/W2017865929","doi":"https://doi.org/10.1137/07068744x","title":"On Analysis Error Covariances in Variational Data Assimilation","display_name":"On Analysis Error Covariances in Variational Data Assimilation","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2017865929","doi":"https://doi.org/10.1137/07068744x","mag":"2017865929"},"language":"en","primary_location":{"id":"doi:10.1137/07068744x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068744x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5007632328","display_name":"Igor Gejadze","orcid":"https://orcid.org/0000-0003-1941-5110"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"I. Yu. Gejadze","raw_affiliation_strings":["igor.gejadze@strath.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"igor.gejadze@strath.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032015670","display_name":"Fran\u00e7ois\u2010Xavier Le Dimet","orcid":"https://orcid.org/0000-0002-3204-1275"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F.-X. Le Dimet","raw_affiliation_strings":["ledimet@imag.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"ledimet@imag.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017189750","display_name":"V. P. Shutyaev","orcid":"https://orcid.org/0000-0002-5932-4478"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Shutyaev","raw_affiliation_strings":["shutyaev@inm.ras.ru#TAB#"],"affiliations":[{"raw_affiliation_string":"shutyaev@inm.ras.ru#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007632328"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1002,"has_fulltext":false,"cited_by_count":86,"citation_normalized_percentile":{"value":0.93218025,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"4","first_page":"1847","last_page":"1874"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"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/T10029","display_name":"Climate variability and models","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.8818743228912354},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8726270198822021},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.7993695735931396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7061614990234375},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6037985682487488},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5929681658744812},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5761302709579468},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4605620801448822},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4392821788787842},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.41433918476104736},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.4106147885322571},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38736844062805176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21626731753349304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20721787214279175}],"concepts":[{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.8818743228912354},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8726270198822021},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.7993695735931396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7061614990234375},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6037985682487488},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5929681658744812},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5761302709579468},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4605620801448822},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4392821788787842},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.41433918476104736},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.4106147885322571},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38736844062805176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21626731753349304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20721787214279175},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/07068744x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068744x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:16313","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/404860.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:HAL:inria-00391893v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00391893","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 2008, 30 (4), pp.1847-1874. &#x27E8;10.1137/07068744X&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W27530157","https://openalex.org/W140544284","https://openalex.org/W790451676","https://openalex.org/W1534488808","https://openalex.org/W1537335979","https://openalex.org/W1968172751","https://openalex.org/W1971621572","https://openalex.org/W1978344088","https://openalex.org/W1984310153","https://openalex.org/W1989575957","https://openalex.org/W2009511046","https://openalex.org/W2014168697","https://openalex.org/W2041863660","https://openalex.org/W2051434435","https://openalex.org/W2058507064","https://openalex.org/W2069828243","https://openalex.org/W2078031695","https://openalex.org/W2091917610","https://openalex.org/W2095921725","https://openalex.org/W2103459312","https://openalex.org/W2117876399","https://openalex.org/W2129835183","https://openalex.org/W2157098139","https://openalex.org/W2169562507","https://openalex.org/W2249032623","https://openalex.org/W2317957800","https://openalex.org/W2469715737","https://openalex.org/W2485377127","https://openalex.org/W2495680075","https://openalex.org/W2905727502","https://openalex.org/W3173138228","https://openalex.org/W4232424818","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1983117412","https://openalex.org/W2026245502","https://openalex.org/W4221162014","https://openalex.org/W1964096161","https://openalex.org/W3091576739","https://openalex.org/W2981801659","https://openalex.org/W2039312875","https://openalex.org/W4318192194","https://openalex.org/W4307537123","https://openalex.org/W2056914158"],"abstract_inverted_index":{"The":[0,25,80],"problem":[1,17,72],"of":[2,36,67,108],"variational":[3],"data":[4,39,70,94],"assimilation":[5,71,95],"for":[6,27],"a":[7,52],"nonlinear":[8,53,99],"evolution":[9],"model":[10,78],"is":[11,31,46,83,102],"formulated":[12],"as":[13],"an":[14,68],"optimal":[15],"control":[16],"to":[18,48,104],"find":[19],"the":[20,28,34,37,55,64,75,86,92,106,109],"initial":[21],"condition":[22],"function":[23],"(analysis).":[24],"equation":[26,45],"analysis":[29,56],"error":[30,57],"derived":[32],"through":[33],"errors":[35],"input":[38],"(background":[40],"and":[41],"observation":[42],"errors).":[43],"This":[44],"used":[47],"show":[49],"that":[50],"in":[51],"case":[54],"covariance":[58],"operator":[59],"can":[60],"be":[61],"approximated":[62],"by":[63,85],"inverse":[65,81],"Hessian":[66,82],"auxiliary":[69,93],"which":[73],"involves":[74],"tangent":[76],"linear":[77],"constraints.":[79],"constructed":[84],"quasi-Newton":[87],"BFGS":[88],"algorithm":[89],"when":[90],"solving":[91],"problem.":[96],"A":[97],"fully":[98],"ensemble":[100],"procedure":[101],"developed":[103],"verify":[105],"accuracy":[107],"proposed":[110],"algorithm.":[111],"Numerical":[112],"examples":[113],"are":[114],"presented.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
