{"id":"https://openalex.org/W2005428526","doi":"https://doi.org/10.1090/s0025-5718-00-01299-0","title":"Approximation orders for natural splines in arbitrary dimensions","display_name":"Approximation orders for natural splines in arbitrary dimensions","publication_year":2000,"publication_date":"2000-10-18","ids":{"openalex":"https://openalex.org/W2005428526","doi":"https://doi.org/10.1090/s0025-5718-00-01299-0","mag":"2005428526"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01299-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01299-0","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01299-0/S0025-5718-00-01299-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01299-0/S0025-5718-00-01299-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088964909","display_name":"Tim Gutzmer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210123467","display_name":"Institut f\u00fcr Angewandte Statistik","ror":"https://ror.org/03abd2075","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210123467"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH","DE"],"is_corresponding":true,"raw_author_name":"Tim Gutzmer","raw_affiliation_strings":["Seminar f\u00c3\u00bcr Angewandte Mathematik, ETH Z\u00c3\u00bcrich, CH-8092 Z\u00c3\u00bcrich","Seminar f\u00fcr Angewandte Mathematik, ETH Z\u00fcrich, CH\u20108092 Z\u00fcrich"],"affiliations":[{"raw_affiliation_string":"Seminar f\u00c3\u00bcr Angewandte Mathematik, ETH Z\u00c3\u00bcrich, CH-8092 Z\u00c3\u00bcrich","institution_ids":["https://openalex.org/I4210123467"]},{"raw_affiliation_string":"Seminar f\u00fcr Angewandte Mathematik, ETH Z\u00fcrich, CH\u20108092 Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210123467","display_name":"Institut f\u00fcr Angewandte Statistik","ror":"https://ror.org/03abd2075","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210123467"]}],"countries":["CH","DE"],"is_corresponding":false,"raw_author_name":"Jens Markus Melenk","raw_affiliation_strings":["Seminar f\u00c3\u00bcr Angewandte Mathematik, ETH Z\u00c3\u00bcrich, CH-8092 Z\u00c3\u00bcrich","Seminar f\u00fcr Angewandte Mathematik, ETH Z\u00fcrich, CH\u20108092 Z\u00fcrich"],"affiliations":[{"raw_affiliation_string":"Seminar f\u00c3\u00bcr Angewandte Mathematik, ETH Z\u00c3\u00bcrich, CH-8092 Z\u00c3\u00bcrich","institution_ids":["https://openalex.org/I4210123467"]},{"raw_affiliation_string":"Seminar f\u00fcr Angewandte Mathematik, ETH Z\u00fcrich, CH\u20108092 Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088964909"],"corresponding_institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210123467"],"apc_list":null,"apc_paid":null,"fwci":0.5538,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66997939,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"70","issue":"234","first_page":"699","last_page":"704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9247000217437744,"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":0.8736727237701416},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.7512600421905518},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.706986665725708},{"id":"https://openalex.org/keywords/box-spline","display_name":"Box spline","score":0.6829670071601868},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5090067386627197},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45026400685310364},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.4256143271923065},{"id":"https://openalex.org/keywords/natural","display_name":"Natural (archaeology)","score":0.41035956144332886},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.2413690686225891},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.228504478931427},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09603339433670044},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.07807394862174988},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04670330882072449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8736727237701416},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.7512600421905518},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.706986665725708},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.6829670071601868},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5090067386627197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45026400685310364},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.4256143271923065},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.41035956144332886},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.2413690686225891},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.228504478931427},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09603339433670044},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.07807394862174988},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04670330882072449},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-00-01299-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01299-0","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01299-0/S0025-5718-00-01299-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.102.7116","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.7116","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01299-0/S0025-5718-00-01299-0.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.6772","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.6772","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-234/S0025-5718-00-01299-0/S0025-5718-00-01299-0.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.43.2706","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.2706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sam.math.ethz.ch/~melenk/approx.ps.Z","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01299-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01299-0","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01299-0/S0025-5718-00-01299-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2005428526.pdf","grobid_xml":"https://content.openalex.org/works/W2005428526.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W63727357","https://openalex.org/W166906646","https://openalex.org/W1481005310","https://openalex.org/W1492326914","https://openalex.org/W2014051441","https://openalex.org/W2035637093","https://openalex.org/W2039980464","https://openalex.org/W2068179746","https://openalex.org/W2494779131","https://openalex.org/W2587718103","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2478648414","https://openalex.org/W2165066371","https://openalex.org/W1633071293","https://openalex.org/W1559256410","https://openalex.org/W2107430952","https://openalex.org/W2905166033","https://openalex.org/W2150799168","https://openalex.org/W2152278269","https://openalex.org/W2014674691","https://openalex.org/W23499285"],"abstract_inverted_index":{"Based":[0],"on":[1],"variational":[2],"properties,":[3],"we":[4],"generalize":[5],"the":[6,10],"approximation":[7],"properties":[8],"of":[9],"univariate":[11],"natural":[12],"cubic":[13],"spline":[14],"to":[15],"splines":[16],"in":[17],"arbitrary":[18],"dimensions.":[19]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
