{"id":"https://openalex.org/W2066409146","doi":"https://doi.org/10.1137/s0036142999360688","title":"Optimal Rational Functions for the Generalized Zolotarev Problem in the Complex Plane","display_name":"Optimal Rational Functions for the Generalized Zolotarev Problem in the Complex Plane","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2066409146","doi":"https://doi.org/10.1137/s0036142999360688","mag":"2066409146"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999360688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999360688","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5090338078","display_name":"B. Le Bailly","orcid":null},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"B. Le Bailly","raw_affiliation_strings":["Universit\u00e9 de Namur"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Namur","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003928058","display_name":"J.-P. Thiran","orcid":null},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. P. Thiran","raw_affiliation_strings":["Universit\u00e9 de Namur"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Namur","institution_ids":["https://openalex.org/I149768937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090338078"],"corresponding_institution_ids":["https://openalex.org/I149768937"],"apc_list":null,"apc_paid":null,"fwci":0.5654,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.65878978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"5","first_page":"1409","last_page":"1424"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9993000030517578,"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":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.8736034035682678},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.838779866695404},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.6923302412033081},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.6721429824829102},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6611641645431519},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5529607534408569},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5354993343353271},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5176334977149963},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46546176075935364},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3579915463924408},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35468846559524536},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3253101706504822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17804715037345886}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8736034035682678},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.838779866695404},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.6923302412033081},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.6721429824829102},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6611641645431519},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5529607534408569},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5354993343353271},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5176334977149963},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46546176075935364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3579915463924408},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35468846559524536},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3253101706504822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17804715037345886},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142999360688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999360688","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:99247","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.2/99247","pdf_url":null,"source":{"id":"https://openalex.org/S4306400166","display_name":"Digital Access to Libraries","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800384882","host_organization_name":"Harris County Public Library","host_organization_lineage":["https://openalex.org/I2800384882"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, Vol. 38, no. 5, p. 1409-1424 (2000)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6499999761581421,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W604181985","https://openalex.org/W648136064","https://openalex.org/W1491365776","https://openalex.org/W1600749473","https://openalex.org/W1975795280","https://openalex.org/W1979084948","https://openalex.org/W1992725728","https://openalex.org/W1997558698","https://openalex.org/W2008848819","https://openalex.org/W2017107439","https://openalex.org/W2032298889","https://openalex.org/W2037589078","https://openalex.org/W2046263770","https://openalex.org/W2051700494","https://openalex.org/W2058769610","https://openalex.org/W2066753524","https://openalex.org/W2067196795","https://openalex.org/W2081128548","https://openalex.org/W2093433489","https://openalex.org/W2094187702","https://openalex.org/W2242107747","https://openalex.org/W4230941884","https://openalex.org/W4235081198"],"related_works":["https://openalex.org/W2152478214","https://openalex.org/W2963699585","https://openalex.org/W2614534673","https://openalex.org/W2066409146","https://openalex.org/W2887252601","https://openalex.org/W1969466213","https://openalex.org/W1974021576","https://openalex.org/W1977563107","https://openalex.org/W2022054586","https://openalex.org/W2096113666"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"long":[3],"recognized":[4],"that":[5,73,152],"the":[6,12,21,58,85,89,104,109,114,123,132,140,146,153,156],"determination":[7],"of":[8,51,54,81,103,135,171],"optimal":[9,124],"parameters":[10],"for":[11,39,168],"classical":[13,157],"alternating":[14],"direction":[15],"implicit":[16],"(ADI)":[17],"method":[18,118],"leads":[19],"to":[20,83,88,107,121,131,145],"Zolotarev":[22,111],"problem":[23,87,112],"\\[":[24],"\\min_{r":[25],"\\in":[26,31,36],"R_{nn}}":[27],"\\frac{\\max":[28],"\\{|r(z)|,":[29,34],"z":[30,35],"E":[32,61],"\\}}{\\min":[33],"F\\}}":[37],"\\]":[38],"disjoint":[40],"compact":[41],"sets":[42],"E,":[43],"F":[44,63,143],"\\subseteq":[45],"\\mathbb{C}$,":[46],"where":[47,60],"Rnn":[48],"isthe":[49],"collection":[50],"rational":[52,125],"functions":[53],"order":[55],"n.":[56,100],"In":[57],"case":[59],"and":[62,97],"are":[64,165],"real":[65,141],"intervals,":[66],"it":[67,79],"was":[68],"more":[69],"recently":[70],"pointed":[71],"out":[72],"if":[74],"they":[75],"have":[76],"different":[77],"lengths,":[78],"is":[80,106,119,128],"interest":[82],"generalize":[84],"foregoing":[86],"set":[90],"Rmn":[91],"with":[92],"unequal":[93],"numerator":[94],"degree":[95,99],"m":[96],"denominator":[98],"The":[101],"object":[102],"paper":[105],"investigate":[108],"generalized":[110],"in":[113],"complex":[115],"plane.":[116],"A":[117],"proposed":[120],"construct":[122],"function,":[126],"which":[127],"then":[129],"applied":[130],"particular":[133],"example":[134],"two":[136],"line":[137],"segments---E":[138],"on":[139,155],"axis,":[142],"parallel":[144],"imaginary":[147],"axis.":[148],"Numerical":[149],"experiments":[150],"show":[151],"improvement":[154],"solution":[158],"may":[159],"be":[160],"amazingly":[161],"great.":[162],"Explicit":[163],"expressions":[164],"also":[166],"provided":[167],"special":[169],"values":[170],"data.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2025-10-10T00:00:00"}