{"id":"https://openalex.org/W7224015194","doi":"https://doi.org/10.71310/pcam.4-1_75.2026.07","title":"The Squared Norm of the Error Functional for a Third-Derivative Interpolation Formula in a Hilbert Space","display_name":"The Squared Norm of the Error Functional for a Third-Derivative Interpolation Formula in a Hilbert Space","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224015194","doi":"https://doi.org/10.71310/pcam.4-1_75.2026.07"},"language":"en","primary_location":{"id":"doi:10.71310/pcam.4-1_75.2026.07","doi":"https://doi.org/10.71310/pcam.4-1_75.2026.07","is_oa":true,"landing_page_url":"https://doi.org/10.71310/pcam.4-1_75.2026.07","pdf_url":"https://journals.airi.uz/index.php/pvpm/article/download/239/206","source":{"id":"https://openalex.org/S4210197098","display_name":"Problems of Computational and Applied Mathematics","issn_l":"2181-046X","issn":["2181-046X","2181-8460"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Computational and Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://journals.airi.uz/index.php/pvpm/article/download/239/206","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112324522","display_name":"Kh. M. Shadimetov","orcid":"https://orcid.org/0000-0002-4183-6184","observed_orcids":["https://orcid.org/0000-0002-4183-6184"]},"institutions":[{"id":"https://openalex.org/I126419327","display_name":"Tashkent State Transport University","ror":"https://ror.org/00jxr5c40","country_code":"UZ","type":"education","lineage":["https://openalex.org/I126419327"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Kh.M. Shadimetov","raw_affiliation_strings":["Tashkent State Transport University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tashkent State Transport University","institution_ids":["https://openalex.org/I126419327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052281796","display_name":"A.Y. Nafasov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I21256249","display_name":"Tashkent University of Information Technology","ror":"https://ror.org/05987a729","country_code":"UZ","type":"education","lineage":["https://openalex.org/I21256249"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"A.Y. Nafasov","raw_affiliation_strings":["Tashkent University of Information Technologies named after Muhammad al-Khwarizmi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tashkent University of Information Technologies named after Muhammad al-Khwarizmi","institution_ids":["https://openalex.org/I21256249"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.86601913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":"4/1(75)","first_page":"85","last_page":"97"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9916999936103821,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9916999936103821,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0031999999191612005,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0006000000284984708,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extremal-functions","display_name":"extremal functions","score":0.9380000233650208},{"id":"https://openalex.org/keywords/kernel-functions","display_name":"kernel functions","score":0.531000018119812},{"id":"https://openalex.org/keywords/optimal-coefficients","display_name":"optimal coefficients","score":0.4300000071525574},{"id":"https://openalex.org/keywords/sobolev-spaces","display_name":"Sobolev spaces","score":0.6480000019073486},{"id":"https://openalex.org/keywords/polynomial-exactness","display_name":"polynomial exactness","score":0.5989999771118164},{"id":"https://openalex.org/keywords/exponential-function","display_name":"exponential function","score":0.6029999852180481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8700000047683716},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.715399980545044},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5450999736785889},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.49160000681877136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4848000109195709},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.478300005197525},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.4659000039100647},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.45809999108314514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45669999718666077},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.45239999890327454},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.45159998536109924},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.4383000135421753},{"id":"https://openalex.org/C75413324","wikidata":"https://www.wikidata.org/wiki/Q1530791","display_name":"Square-integrable function","level":2,"score":0.42969998717308044},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.38999998569488525},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.3837999999523163},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"score":0.3822999894618988},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.3817000091075897},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C119768884","wikidata":"https://www.wikidata.org/wiki/Q7597108","display_name":"Stairstep interpolation","level":4,"score":0.3021000027656555},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.27900001406669617}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.71310/pcam.4-1_75.2026.07","doi":"https://doi.org/10.71310/pcam.4-1_75.2026.07","is_oa":true,"landing_page_url":"https://doi.org/10.71310/pcam.4-1_75.2026.07","pdf_url":"https://journals.airi.uz/index.php/pvpm/article/download/239/206","source":{"id":"https://openalex.org/S4210197098","display_name":"Problems of Computational and Applied Mathematics","issn_l":"2181-046X","issn":["2181-046X","2181-8460"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Computational and Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ojs2.journals.airi.uz:article/239","doi":null,"is_oa":true,"landing_page_url":"https://journals.airi.uz/index.php/pvpm/article/view/239","pdf_url":null,"source":{"id":"https://openalex.org/S4210197098","display_name":"Problems of Computational and Applied Mathematics","issn_l":"2181-046X","issn":["2181-046X","2181-8460"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2181-8460","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.71310/pcam.4-1_75.2026.07","doi":"https://doi.org/10.71310/pcam.4-1_75.2026.07","is_oa":true,"landing_page_url":"https://doi.org/10.71310/pcam.4-1_75.2026.07","pdf_url":"https://journals.airi.uz/index.php/pvpm/article/download/239/206","source":{"id":"https://openalex.org/S4210197098","display_name":"Problems of Computational and Applied Mathematics","issn_l":"2181-046X","issn":["2181-046X","2181-8460"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224015194.pdf","grobid_xml":"https://content.openalex.org/works/W7224015194.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7162295269","https://openalex.org/W7217943569","https://openalex.org/W7217791938","https://openalex.org/W4391297331","https://openalex.org/W4407553865","https://openalex.org/W3014958690","https://openalex.org/W4411231589","https://openalex.org/W7204954964","https://openalex.org/W7140193840","https://openalex.org/W7223813204"],"abstract_inverted_index":{"This":[0,218],"work":[1],"is":[2,24,58,63,99,112,156,162,207,232],"devoted":[3],"to":[4,40,69,152,234],"the":[5,20,27,30,34,47,70,80,91,96,107,110,115,121,124,130,153,173,176,184,190,198,201,204,212,216,222,228,236,240],"construction":[6],"of":[7,33,49,95,109,117,123,175,200,203,211,215,239],"an":[8,75,148],"optimal":[9,143,237],"interpolation":[10,54,97,146,191,241],"formula":[11,55,98,111],"for":[12,66,74,141,197],"functions":[13,85],"defined":[14],"on":[15,129,226],"a":[16,87,167,193],"finite":[17],"interval":[18],"in":[19,36,120,209],"Hilbert":[21,126],"space,":[22],"which":[23,227],"characterized":[25,100],"by":[26,46,83,101,114,134,164,172,189],"requirement":[28],"that":[29,61],"third-order":[31],"derivative":[32],"function":[35,119,150,170,181],"this":[37,118,179],"space":[38],"needs":[39],"be":[41],"absolutely":[42],"continuous":[43],"and":[44,73,79,106,138,145,158],"integrable":[45],"square":[48,199],"its":[50,102,159],"fourth-order":[51],"derivative.":[52],"The":[53,93],"under":[56],"consideration":[57],"constructed":[59],"so":[60],"it":[62],"exact":[64,160],"both":[65],"polynomials":[67],"up":[68],"second":[71],"degree":[72],"invariant":[76],"exponential":[77],"function,":[78],"subspace":[81],"covered":[82],"these":[84],"plays":[86],"central":[88],"role":[89],"throughout":[90],"construction.":[92],"accuracy":[94],"corresponding":[103],"error":[104,154,205],"functional,":[105],"quality":[108],"measured":[113],"norm":[116,202],"conjugate":[122],"underlying":[125],"space.":[127,177],"Based":[128],"variational":[131],"approach":[132],"developed":[133],"S.":[135],"L.":[136],"Sobolev":[137],"his":[139],"school":[140],"constructing":[142],"quadrature":[144],"formulas,":[147],"extremal":[149,180],"related":[151],"functional":[155,206],"introduced,":[157],"expression":[161,196,219],"obtained":[163,208],"convolution":[165],"with":[166,183],"special":[168],"kernel":[169],"determined":[171],"structure":[174],"Using":[178],"together":[182],"discrete":[185],"orthogonality":[186],"conditions":[187],"satisfied":[188],"formula,":[192],"precise":[194],"closed-form":[195],"terms":[210],"unknown":[213],"coefficients":[214,238],"formula.":[217,242],"serves":[220],"as":[221],"main":[223],"initial":[224],"result":[225],"subsequent":[229],"minimization":[230],"problem":[231],"based":[233],"find":[235]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-28T00:00:00"}