{"id":"https://openalex.org/W2076577157","doi":"https://doi.org/10.1007/s10208-005-0197-7","title":"Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions","display_name":"Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions","publication_year":2006,"publication_date":"2006-06-28","ids":{"openalex":"https://openalex.org/W2076577157","doi":"https://doi.org/10.1007/s10208-005-0197-7","mag":"2076577157"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-005-0197-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-005-0197-7","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/50819","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109483006","display_name":"Francis J. Narcowich","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Francis J. Narcowich","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103047873","display_name":"Xingping Sun","orcid":"https://orcid.org/0000-0001-7117-6087"},"institutions":[{"id":"https://openalex.org/I119942284","display_name":"Missouri State University","ror":"https://ror.org/01d2sez20","country_code":"US","type":"education","lineage":["https://openalex.org/I119942284"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xingping Sun","raw_affiliation_strings":["Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA","Department of Mathematics , Southwest Missouri State University , Springfield, MO, 65804, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA","institution_ids":["https://openalex.org/I119942284"]},{"raw_affiliation_string":"Department of Mathematics , Southwest Missouri State University , Springfield, MO, 65804, USA","institution_ids":["https://openalex.org/I119942284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103352171","display_name":"J. D. Ward","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph D. Ward","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066096555","display_name":"Holger Wendland","orcid":"https://orcid.org/0000-0002-9614-5321"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Wendland","raw_affiliation_strings":["Universitat Gottingen, Lotzestrasse 16-18, D-37083, Gottingen, Germany","Universit\u00e4t G\u00f6ttingen, Lotzestrasse 16-18, D-37083, G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"Universitat Gottingen, Lotzestrasse 16-18, D-37083, Gottingen, Germany","institution_ids":["https://openalex.org/I74656192"]},{"raw_affiliation_string":"Universit\u00e4t G\u00f6ttingen, Lotzestrasse 16-18, D-37083, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109483006"],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.4136,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.92069198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"7","issue":"3","first_page":"369","last_page":"390"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7959017753601074},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7919635772705078},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7883236408233643},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6644071936607361},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46367570757865906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42229756712913513},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.42163345217704773},{"id":"https://openalex.org/keywords/nyquist-frequency","display_name":"Nyquist frequency","score":0.41732320189476013},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3654719591140747},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1316644847393036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0746990442276001}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7959017753601074},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7919635772705078},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7883236408233643},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6644071936607361},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46367570757865906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42229756712913513},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.42163345217704773},{"id":"https://openalex.org/C98273374","wikidata":"https://www.wikidata.org/wiki/Q1501757","display_name":"Nyquist frequency","level":3,"score":0.41732320189476013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3654719591140747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1316644847393036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0746990442276001},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10208-005-0197-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-005-0197-7","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:bearworks.missouristate.edu:articles-cnas-1732","is_oa":false,"landing_page_url":"https://bearworks.missouristate.edu/articles-cnas/733","pdf_url":null,"source":{"id":"https://openalex.org/S4377196450","display_name":"BearWorks (Missouri State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119942284","host_organization_name":"Missouri State University","host_organization_lineage":["https://openalex.org/I119942284"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"College of Natural and Applied Sciences","raw_type":"text"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/50819","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/50819","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal_article"}],"best_oa_location":{"id":"pmh:oai:publications.goettingen-research-online.de:2/50819","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/50819","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal_article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W33346649","https://openalex.org/W137098816","https://openalex.org/W166906646","https://openalex.org/W207290963","https://openalex.org/W311724416","https://openalex.org/W319411128","https://openalex.org/W1495010649","https://openalex.org/W1547987345","https://openalex.org/W1597209545","https://openalex.org/W1676717239","https://openalex.org/W1963785789","https://openalex.org/W1973878509","https://openalex.org/W1981387538","https://openalex.org/W1991137104","https://openalex.org/W1993806324","https://openalex.org/W1995274909","https://openalex.org/W1995990042","https://openalex.org/W2021828492","https://openalex.org/W2023638740","https://openalex.org/W2039343706","https://openalex.org/W2040314635","https://openalex.org/W2041620610","https://openalex.org/W2052524535","https://openalex.org/W2060141144","https://openalex.org/W2071343184","https://openalex.org/W2072146174","https://openalex.org/W2074029034","https://openalex.org/W2081338783","https://openalex.org/W2084196626","https://openalex.org/W2087948458","https://openalex.org/W2161591817","https://openalex.org/W2313689636","https://openalex.org/W3106701803"],"related_works":["https://openalex.org/W4299978068","https://openalex.org/W2950745223","https://openalex.org/W2164189677","https://openalex.org/W4301407218","https://openalex.org/W4388311156","https://openalex.org/W4296771954","https://openalex.org/W4390620896","https://openalex.org/W2963735960","https://openalex.org/W1869870390","https://openalex.org/W2811033119"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":9}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}