{"id":"https://openalex.org/W3169391663","doi":"https://doi.org/10.1134/s199542392101002x","title":"On Optimal Approximation of Geophysical Fields","display_name":"On Optimal Approximation of Geophysical Fields","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3169391663","doi":"https://doi.org/10.1134/s199542392101002x","mag":"3169391663"},"language":"en","primary_location":{"id":"doi:10.1134/s199542392101002x","doi":"https://doi.org/10.1134/s199542392101002x","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s199542392101002x","pdf_url":null,"source":{"id":"https://openalex.org/S2259906","display_name":"Numerical Analysis and Applications","issn_l":"1560-7526","issn":["1560-7526","1995-4239","1995-4247"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-1","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Analysis and Applications","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W3169391663"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5080570565","display_name":"\u0418. \u0412. \u0411\u043e\u0439\u043a\u043e\u0432","orcid":"https://orcid.org/0000-0002-6980-933X","observed_orcids":["https://orcid.org/0000-0002-6980-933X"]},"institutions":[{"id":"https://openalex.org/I114616248","display_name":"Penza State University","ror":"https://ror.org/056r5vk88","country_code":"RU","type":"education","lineage":["https://openalex.org/I114616248"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"I. V. Boikov","raw_affiliation_strings":["Penza State University, Penza, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Penza State University, Penza, Russia","institution_ids":["https://openalex.org/I114616248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042651040","display_name":"\u0420\u044f\u0437\u0430\u043d\u0446\u0435\u0432 \u0412\u043b\u0430\u0434\u0438\u043c\u0438\u0440 \u0410\u043d\u0434\u0440\u0435\u0435\u0432\u0438\u0447","orcid":"https://orcid.org/0000-0003-0875-9823","observed_orcids":["https://orcid.org/0000-0003-0875-9823"]},"institutions":[{"id":"https://openalex.org/I114616248","display_name":"Penza State University","ror":"https://ror.org/056r5vk88","country_code":"RU","type":"education","lineage":["https://openalex.org/I114616248"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"V. A. Ryazantsev","raw_affiliation_strings":["Penza State University, Penza, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Penza State University, Penza, Russia","institution_ids":["https://openalex.org/I114616248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042651040","https://openalex.org/A5080570565"],"corresponding_institution_ids":["https://openalex.org/I114616248"],"apc_list":null,"apc_paid":null,"fwci":0.3642,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.43373827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"14","issue":"1","first_page":"13","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.8090999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.8090999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.11150000244379044,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.009800000116229057,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/best-approximation","display_name":"best approximation","score":0.9739999771118164},{"id":"https://openalex.org/keywords/geophysical-fields","display_name":"geophysical fields","score":0.9710000157356262},{"id":"https://openalex.org/keywords/gravitational-field","display_name":"gravity field","score":0.8119999766349792},{"id":"https://openalex.org/keywords/temperature-distribution","display_name":"temperature distribution","score":0.9919999837875366},{"id":"https://openalex.org/keywords/heat-equation","display_name":"heat equation","score":0.9409999847412109},{"id":"https://openalex.org/keywords/kolmogorov-widths","display_name":"Kolmogorov widths","score":0.9039999842643738},{"id":"https://openalex.org/keywords/function-classes","display_name":"function classes","score":0.7089999914169312},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.4129999876022339},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.7400000095367432},{"id":"https://openalex.org/keywords/multivariate-approximation","display_name":"multivariate approximation","score":0.8709999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6037935614585876},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5958559513092041},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5397596955299377},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.5148176550865173},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5009119510650635},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48263344168663025},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.47431159019470215},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.45265334844589233},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.4376526176929474},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4023182988166809},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2084941565990448},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17686006426811218},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.16243994235992432},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16070055961608887},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.11016777157783508},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s199542392101002x","doi":"https://doi.org/10.1134/s199542392101002x","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s199542392101002x","pdf_url":null,"source":{"id":"https://openalex.org/S2259906","display_name":"Numerical Analysis and Applications","issn_l":"1560-7526","issn":["1560-7526","1995-4239","1995-4247"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-1","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1533889494","https://openalex.org/W1965720095","https://openalex.org/W1973513227","https://openalex.org/W1979956500","https://openalex.org/W2035242097","https://openalex.org/W2157728669","https://openalex.org/W2159348875","https://openalex.org/W2163050067","https://openalex.org/W2270944735","https://openalex.org/W2290938292","https://openalex.org/W2321629260","https://openalex.org/W2666251334","https://openalex.org/W4285719527","https://openalex.org/W6817900367"],"related_works":["https://openalex.org/W138945467","https://openalex.org/W4256036385","https://openalex.org/W2159348875","https://openalex.org/W1580942156","https://openalex.org/W2025849594","https://openalex.org/W4402004897","https://openalex.org/W2560948221","https://openalex.org/W4229517884","https://openalex.org/W7220539508","https://openalex.org/W2017975065"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,26],"paper,":[3],"optimal":[4],"methods":[5],"of":[6,8,22,32,52,57,76,86,89,97,102,107],"approximation":[7,33],"some":[9],"geophysical":[10],"fields,":[11,17],"in":[12,72],"particular":[13],"gravitational":[14],"and":[15,62],"thermal":[16,37],"are":[18,60,78,91],"considered.":[19],"A":[20],"review":[21],"the":[23,35,55,67,70,73,83,98,108],"results":[24],"on":[25],"problem":[27],"is":[28,47,111],"presented.":[29,112],"An":[30],"algorithm":[31],"for":[34,82],"multidimensional":[36],"fields":[38],"described":[39],"by":[40],"a":[41,94,104],"heat":[42,58],"equation":[43],"with":[44],"constant":[45],"coefficients":[46],"developed.":[48],"For":[49,93],"this,":[50],"classes":[51,71,88,101],"functions":[53,68,90],"including":[54],"solutions":[56],"equations":[59],"introduced,":[61],"continuous":[63],"splines":[64],"uniformly":[65],"approximating":[66],"from":[69],"whole":[74],"domain":[75],"definition":[77],"constructed.":[79],"Upper":[80],"bounds":[81],"Kolmogorov":[84,109],"widths":[85],"these":[87],"given.":[92],"wider":[95],"class":[96],"thus":[99],"introduced":[100],"functions,":[103],"lower":[105],"estimate":[106],"width":[110]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2021-06-22T00:00:00"}