{"id":"https://openalex.org/W1985005735","doi":"https://doi.org/10.1137/110825121","title":"On Computation of the Design Function Gradient for the Sensor-Location Problem in Variational Data Assimilation","display_name":"On Computation of the Design Function Gradient for the Sensor-Location Problem in Variational Data Assimilation","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1985005735","doi":"https://doi.org/10.1137/110825121","mag":"1985005735"},"language":"en","primary_location":{"id":"doi:10.1137/110825121","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825121","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":"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":2,"corresponding_author_ids":["https://openalex.org/A5007632328"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.06250672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"34","issue":"2","first_page":"B127","last_page":"B147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9995999932289124,"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":0.9995999932289124,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9948999881744385,"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/T10644","display_name":"Cryospheric studies and observations","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.892880916595459},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.6395084857940674},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6222280263900757},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.556669294834137},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5540211200714111},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.535747230052948},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5230665802955627},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4671682119369507},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43981409072875977},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4317648112773895},{"id":"https://openalex.org/keywords/adjoint-equation","display_name":"Adjoint equation","score":0.42529192566871643},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.42178183794021606},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.41772258281707764},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4106371998786926},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37760165333747864},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.30579978227615356},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28324228525161743},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21207469701766968},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.09077125787734985}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.892880916595459},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.6395084857940674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6222280263900757},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.556669294834137},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5540211200714111},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.535747230052948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5230665802955627},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4671682119369507},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43981409072875977},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4317648112773895},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.42529192566871643},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.42178183794021606},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.41772258281707764},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4106371998786926},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37760165333747864},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.30579978227615356},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28324228525161743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21207469701766968},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.09077125787734985},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110825121","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825121","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:42545","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/42545/","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1964857401","https://openalex.org/W1988665016","https://openalex.org/W1994014585","https://openalex.org/W2017865929","https://openalex.org/W2036694594","https://openalex.org/W2038711318","https://openalex.org/W2052712510","https://openalex.org/W2071759076","https://openalex.org/W2078031695","https://openalex.org/W2079159741","https://openalex.org/W2080607773","https://openalex.org/W2093359910","https://openalex.org/W2099425512","https://openalex.org/W2106954701","https://openalex.org/W2139004160","https://openalex.org/W2141702337","https://openalex.org/W2156688520","https://openalex.org/W2167539472","https://openalex.org/W2173770184","https://openalex.org/W2175104113","https://openalex.org/W2179229003","https://openalex.org/W4229880037"],"related_works":["https://openalex.org/W4297883503","https://openalex.org/W2356977358","https://openalex.org/W2316769148","https://openalex.org/W3199158697","https://openalex.org/W263682811","https://openalex.org/W1994333428","https://openalex.org/W2355987247","https://openalex.org/W2067693696","https://openalex.org/W3194213170","https://openalex.org/W4200512840"],"abstract_inverted_index":{"The":[0,50,142],"optimal":[1],"sensor-location":[2,63],"problem":[3,24,30],"is":[4,25,65,85,114,147],"considered":[5],"in":[6,149],"the":[7,32,37,41,45,53,56,62,68,71,78,90,94,108,122,125,132,140,145,150,159,163,167],"framework":[8],"of":[9,40,44,55,93,103,124,131,144,162],"variational":[10],"data":[11,46,118],"assimilation":[12,47],"for":[13,31,52,77,82,158],"a":[14,100],"large-scale":[15,83],"dynamical":[16],"model":[17,135],"governed":[18],"by":[19,99,107],"partial":[20],"differential":[21],"equations.":[22],"This":[23,87],"formulated":[26],"as":[27],"an":[28],"optimization":[29,161,170],"design":[33,57,164],"function":[34,58,165],"defined":[35,98],"on":[36],"limited-memory":[38,95],"approximation":[39],"inverse":[42,96],"Hessian":[43,72,97],"cost":[48],"function.":[49],"expression":[51],"gradient":[54,79],"with":[59],"respect":[60],"to":[61,70,138],"coordinates":[64],"derived":[66],"via":[67],"adjoint":[69],"derivative.":[73],"An":[74],"efficient":[75],"algorithm":[76,88],"evaluation":[80],"suitable":[81],"applications":[84],"suggested.":[86],"exploits":[89],"special":[91],"structure":[92],"small":[101],"number":[102],"Ritz":[104,126],"pairs":[105],"obtained":[106],"Lanczos":[109],"method.":[110],"If":[111],"additional":[112,129],"memory":[113],"allocated":[115],"and":[116],"certain":[117],"are":[119,136],"stored":[120],"during":[121],"computation":[123],"pairs,":[127],"no":[128],"runs":[130],"tangent":[133],"linear":[134],"required":[137],"evaluate":[139],"gradient.":[141],"accuracy":[143],"gradients":[146,154],"checked":[148],"numerical":[151],"experiments.":[152],"These":[153],"can":[155],"be":[156],"used":[157],"gradient-based":[160],"within":[166],"chosen":[168],"global":[169],"procedure.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}