{"id":"https://openalex.org/W1982363352","doi":"https://doi.org/10.1090/s0025-5718-05-01790-4","title":"Gr\u00f6bner bases and generalized Pad\u00e9 approximation","display_name":"Gr\u00f6bner bases and generalized Pad\u00e9 approximation","publication_year":2005,"publication_date":"2005-10-12","ids":{"openalex":"https://openalex.org/W1982363352","doi":"https://doi.org/10.1090/s0025-5718-05-01790-4","mag":"1982363352"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01790-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01790-4","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01790-4/S0025-5718-05-01790-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01790-4/S0025-5718-05-01790-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074088515","display_name":"Jeffrey B. Farr","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Jeffrey Farr","raw_affiliation_strings":["Centre for Experimental and Constructive Mathematics (CECM) and Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6"],"affiliations":[{"raw_affiliation_string":"Centre for Experimental and Constructive Mathematics (CECM) and Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008978009","display_name":"Shuhong Gao","orcid":"https://orcid.org/0000-0002-0937-1727"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuhong Gao","raw_affiliation_strings":["Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","institution_ids":["https://openalex.org/I8078737"]},{"raw_affiliation_string":"Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074088515"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":0.3367,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.5968222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"75","issue":"253","first_page":"461","last_page":"473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9764000177383423,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9072819948196411},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6244550347328186},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5786350965499878},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4843812882900238},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.47483569383621216},{"id":"https://openalex.org/keywords/standard-basis","display_name":"Standard basis","score":0.44290757179260254},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.434510737657547},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28067338466644287},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08536019921302795},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07681715488433838}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9072819948196411},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6244550347328186},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5786350965499878},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4843812882900238},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47483569383621216},{"id":"https://openalex.org/C41054515","wikidata":"https://www.wikidata.org/wiki/Q2000912","display_name":"Standard basis","level":2,"score":0.44290757179260254},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.434510737657547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28067338466644287},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08536019921302795},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07681715488433838},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-05-01790-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01790-4","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01790-4/S0025-5718-05-01790-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.104.8091","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.8091","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/2006-75-253/S0025-5718-05-01790-4/S0025-5718-05-01790-4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.4621","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.4621","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.clemson.edu/faculty/Gao/papers/interp.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.68.7923","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.68.7923","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.clemson.edu/faculty/Gao/papers/interp.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01790-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01790-4","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01790-4/S0025-5718-05-01790-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2271204313","display_name":"Algorithms for polynomial systems","funder_award_id":"0302549","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320322675","display_name":"Mitacs","ror":"https://ror.org/00cjrc276"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1982363352.pdf","grobid_xml":"https://content.openalex.org/works/W1982363352.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W116293564","https://openalex.org/W1483218536","https://openalex.org/W1493026726","https://openalex.org/W1524738630","https://openalex.org/W1550054248","https://openalex.org/W1561016548","https://openalex.org/W1871606885","https://openalex.org/W1963636946","https://openalex.org/W1963695291","https://openalex.org/W1975653056","https://openalex.org/W1982662469","https://openalex.org/W2011174964","https://openalex.org/W2032431003","https://openalex.org/W2038436234","https://openalex.org/W2079751279","https://openalex.org/W2145738710","https://openalex.org/W2264065105","https://openalex.org/W2319466955","https://openalex.org/W4237780066","https://openalex.org/W4292096448","https://openalex.org/W4298289021"],"related_works":["https://openalex.org/W1483236051","https://openalex.org/W2951644484","https://openalex.org/W4294910641","https://openalex.org/W4313233864","https://openalex.org/W4298043651","https://openalex.org/W3100582318","https://openalex.org/W2068435201","https://openalex.org/W2026118429","https://openalex.org/W2372890883","https://openalex.org/W2949941204"],"abstract_inverted_index":{"It":[0],"is":[1,17,37,49],"shown":[2],"how":[3],"to":[4,28,40],"find":[5],"general":[6],"multivariate":[7],"Pad\u00e9":[8],"approximation":[9],"using":[10],"the":[11,33,41,45,53,58],"Gr\u00f6bner":[12,46],"basis":[13,47],"technique.":[14],"This":[15],"method":[16],"more":[18,50],"flexible":[19],"than":[20,52],"previous":[21],"approaches,":[22],"and":[23],"several":[24],"examples":[25],"are":[26],"given":[27],"illustrate":[29],"this":[30],"advantage.":[31],"When":[32],"number":[34],"of":[35,43],"variables":[36],"small":[38],"compared":[39],"degree":[42],"approximation,":[44],"technique":[48],"efficient":[51],"linear":[54],"algebra":[55],"methods":[56],"in":[57],"literature.":[59]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":10}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
