{"id":"https://openalex.org/W1970298187","doi":"https://doi.org/10.1007/bf02124752","title":"A condition of Schoenberg-Whitney type for multivariate spline interpolation","display_name":"A condition of Schoenberg-Whitney type for multivariate spline interpolation","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W1970298187","doi":"https://doi.org/10.1007/bf02124752","mag":"1970298187"},"language":"en","primary_location":{"id":"doi:10.1007/bf02124752","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02124752","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","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/A5045699413","display_name":"Manfred Sommer","orcid":"https://orcid.org/0009-0002-8094-0838"},"institutions":[{"id":"https://openalex.org/I199417121","display_name":"Catholic University of Eichst\u00e4tt-Ingolstadt","ror":"https://ror.org/00mx91s63","country_code":"DE","type":"education","lineage":["https://openalex.org/I199417121"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Manfred Sommer","raw_affiliation_strings":["Mathematisch-Geographische Fakult\u00e4t, Katholische Universit\u00e4t Eichst\u00e4tt, D-85071, Eichst\u00e4tt, Germany","Mathematisch-Geographische Fakult\u00e4t, Katholische Universit\u00e4t Eichst\u00e4tt, Eichst\u00e4tt, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisch-Geographische Fakult\u00e4t, Katholische Universit\u00e4t Eichst\u00e4tt, D-85071, Eichst\u00e4tt, Germany","institution_ids":["https://openalex.org/I199417121"]},{"raw_affiliation_string":"Mathematisch-Geographische Fakult\u00e4t, Katholische Universit\u00e4t Eichst\u00e4tt, Eichst\u00e4tt, Germany","institution_ids":["https://openalex.org/I199417121"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111999858","display_name":"Hans Strau\u00df","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans Strauss","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Erlangen-N\u00fcrnberg, D-91058, Erlangen, Germany","Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Erlangen-N\u00fcrnberg, D-91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany#TAB#","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045699413"],"corresponding_institution_ids":["https://openalex.org/I199417121"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.892,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.88871394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"5","issue":"1","first_page":"381","last_page":"397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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/mathematics","display_name":"Mathematics","score":0.8317590951919556},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6562480926513672},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.6293148994445801},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.6159802079200745},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5538665652275085},{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.5463802814483643},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5134240388870239},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.4897580146789551},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.469329297542572},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.43687495589256287},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.43469634652137756},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4165632128715515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3986368775367737},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37681034207344055},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37152111530303955},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3512687087059021},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10557594895362854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09222173690795898},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07847189903259277},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.07724577188491821},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.06661832332611084},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.06366488337516785},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.057822197675704956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8317590951919556},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6562480926513672},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.6293148994445801},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.6159802079200745},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5538665652275085},{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.5463802814483643},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5134240388870239},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.4897580146789551},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.469329297542572},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.43687495589256287},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.43469634652137756},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4165632128715515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3986368775367737},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37681034207344055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37152111530303955},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3512687087059021},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10557594895362854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09222173690795898},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07847189903259277},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.07724577188491821},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.06661832332611084},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.06366488337516785},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.057822197675704956},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02124752","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02124752","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W194866236","https://openalex.org/W1966055183","https://openalex.org/W1966342431","https://openalex.org/W1975947534","https://openalex.org/W2011099190","https://openalex.org/W2052019487","https://openalex.org/W2055176911","https://openalex.org/W2062261913","https://openalex.org/W2090344516","https://openalex.org/W4233782503"],"related_works":["https://openalex.org/W4237388375","https://openalex.org/W2354378723","https://openalex.org/W4244651132","https://openalex.org/W287160455","https://openalex.org/W2360151650","https://openalex.org/W2391374853","https://openalex.org/W4313680078","https://openalex.org/W4312826909","https://openalex.org/W1565653811","https://openalex.org/W2365148738"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}