{"id":"https://openalex.org/W2133186020","doi":"https://doi.org/10.1137/0917061","title":"A Convolution Algorithm with Application to Data Assimilation","display_name":"A Convolution Algorithm with Application to Data Assimilation","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2133186020","doi":"https://doi.org/10.1137/0917061","mag":"2133186020"},"language":"en","primary_location":{"id":"doi:10.1137/0917061","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0917061","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/A5071487639","display_name":"Ranjit M. Passi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ranjit M. Passi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111536206","display_name":"Robert K. Goodrich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Kent Goodrich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060887630","display_name":"Mark A. Limber","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Limber","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089947098","display_name":"John Derber","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John C. Derber","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071487639"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16996159,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"4","first_page":"942","last_page":"955"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9991999864578247,"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":0.9991999864578247,"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/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9943000078201294,"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/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7109899520874023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6067162156105042},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.5581783652305603},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5248177647590637},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4694485366344452},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.45605677366256714},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4518047869205475},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4433175027370453},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.43083661794662476},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3837861120700836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27049097418785095},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1169443130493164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7109899520874023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6067162156105042},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.5581783652305603},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5248177647590637},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4694485366344452},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.45605677366256714},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4518047869205475},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4433175027370453},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.43083661794662476},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3837861120700836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27049097418785095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1169443130493164},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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":1,"locations":[{"id":"doi:10.1137/0917061","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0917061","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8600000143051147,"display_name":"Life below water","id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1582706191","https://openalex.org/W1979585884","https://openalex.org/W1995788729","https://openalex.org/W2037416330","https://openalex.org/W2041863660","https://openalex.org/W2064261288","https://openalex.org/W2076114194","https://openalex.org/W2158590890","https://openalex.org/W2173377280","https://openalex.org/W2315373644","https://openalex.org/W4256157503","https://openalex.org/W4296357585"],"related_works":["https://openalex.org/W2180954594","https://openalex.org/W2052835778","https://openalex.org/W2049003611","https://openalex.org/W2127804977","https://openalex.org/W2108418243","https://openalex.org/W164103134","https://openalex.org/W2787352659","https://openalex.org/W1970611213","https://openalex.org/W1707372784","https://openalex.org/W2096006843"],"abstract_inverted_index":{"A":[0],"computationally":[1],"efficient":[2],"algorithm":[3,56,85,143,186,198],"to":[4,105,148,168,189],"approximate":[5],"a":[6,47,59,106,114,118,145,162,196],"convolution":[7],"$w":[8],"*":[9],"f$":[10],"is":[11,44],"derived":[12],"when":[13],"the":[14,41,83,95,179,185],"real-valued":[15],"weighting":[16,120],"functions":[17],"w":[18],"are":[19,70],"dimensionally":[20],"separable,":[21],"i.e.,":[22],"$w(x_1":[23],",x_2":[24],")":[25,34],"=":[26,35,67,123],"w_1":[27],"(x_1":[28],")w_2":[29],"(x_2":[30],")$":[31],"and":[32,40,89,99,154,201],"$w(x_k":[33],"w(":[36],"-":[37,126,132],"x_k":[38],")$,":[39],"function":[42,121],"$f(i,j)$":[43],"defined":[45],"on":[46,79,94],"discrete":[48],"integer":[49],"lattice":[50],"in":[51,113,152],"$\\mathcal":[52],"{R}^2":[53],"$.":[54],"The":[55,141],"consists":[57],"of":[58,61,72,86,161,178,199],"product":[60],"operator":[62],"polynomials":[63],"$P_k":[64],"(D_k":[65],"),k":[66],"1,2$,":[68],"which":[69],"composed":[71],"simple":[73],"averaging":[74],"operators":[75],"$D_k":[76],"$":[77],"operating":[78],"f.":[80],"It":[81],"generalizes":[82],"smoothing":[84],"Goodrich,":[87],"Passi,":[88],"Limber":[90],"[Proc.":[91],"24th":[92],"Symposium":[93],"Interface:":[96],"Computing":[97],"Science":[98],"Statistics,":[100],"1992]":[101],"for":[102,175],"data":[103,149,167],"constrained":[104],"uniformly":[107],"spaced,":[108],"large-dimensioned":[109],"orthogonal":[110],"grid":[111],"lying":[112],"two-dimensional":[115],"space,":[116],"using":[117],"Gaussian":[119],"$w(r)":[122],"\\exp":[124],"({{":[125],"r^2":[127,133],"}":[128,134],"\\mathord{\\left/":[129],"{\\vphantom":[130],"{{":[131],"{b^2":[135,139],"}}}":[136],"\\right.":[137],"\\kern-\\nulldelimiterspace}":[138],"}})$.":[140],"new":[142],"has":[144],"direct":[146],"application":[147],"assimilation":[150,157],"problems":[151],"meteorology":[153],"oceanography.":[155],"Data":[156],"optimally":[158],"combines":[159],"output":[160],"numerical":[163,176],"model":[164,180],"with":[165,184],"observational":[166],"derive":[169],"more":[170],"accurate":[171],"initial":[172],"conditions":[173],"needed":[174],"integration":[177],"equations.":[181],"Computer":[182],"simulations":[183],"were":[187],"found":[188],"be":[190],"about":[191],"ten":[192],"times":[193],"faster":[194],"than":[195],"comparable":[197],"Derber":[200],"Rosati":[202],"[J.":[203],"Phys.":[204],"Ocean,":[205],"(1989),":[206],"pp.":[207],"1333\u20131347].":[208]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
