{"id":"https://openalex.org/W2018570254","doi":"https://doi.org/10.1137/0215018","title":"Algebraic Computations of Scaled Pad\u00e9 Fractions","display_name":"Algebraic Computations of Scaled Pad\u00e9 Fractions","publication_year":1986,"publication_date":"1986-02-01","ids":{"openalex":"https://openalex.org/W2018570254","doi":"https://doi.org/10.1137/0215018","mag":"2018570254"},"language":"en","primary_location":{"id":"doi:10.1137/0215018","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0215018","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5113571166","display_name":"S. Cabay","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stanley Cabay","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108432179","display_name":"Dong-Koo Choi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dong-Koo Choi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113571166"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3725,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88206698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"1","first_page":"243","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9871000051498413,"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":0.9871000051498413,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9732999801635742,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.7144615054130554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7140159606933594},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.590837299823761},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5362566709518433},{"id":"https://openalex.org/keywords/main-diagonal","display_name":"Main diagonal","score":0.5087025761604309},{"id":"https://openalex.org/keywords/pad\u00e9-approximant","display_name":"Pad\u00e9 approximant","score":0.47938063740730286},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.46216535568237305},{"id":"https://openalex.org/keywords/formal-power-series","display_name":"Formal power series","score":0.45771685242652893},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44744873046875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43219563364982605},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.430957555770874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.12168848514556885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09819602966308594}],"concepts":[{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7144615054130554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7140159606933594},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.590837299823761},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5362566709518433},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.5087025761604309},{"id":"https://openalex.org/C153150388","wikidata":"https://www.wikidata.org/wiki/Q2452504","display_name":"Pad\u00e9 approximant","level":2,"score":0.47938063740730286},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.46216535568237305},{"id":"https://openalex.org/C151746172","wikidata":"https://www.wikidata.org/wiki/Q1003025","display_name":"Formal power series","level":3,"score":0.45771685242652893},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44744873046875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43219563364982605},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.430957555770874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.12168848514556885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09819602966308594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0215018","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0215018","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1538558557","https://openalex.org/W1655990431","https://openalex.org/W1982661201","https://openalex.org/W2001224529","https://openalex.org/W2011850206","https://openalex.org/W2019320174","https://openalex.org/W2034633383","https://openalex.org/W2058694935","https://openalex.org/W2083658187","https://openalex.org/W2095018839","https://openalex.org/W2100279776","https://openalex.org/W2123161682"],"related_works":["https://openalex.org/W2375855279","https://openalex.org/W2112811681","https://openalex.org/W2092173841","https://openalex.org/W2084989833","https://openalex.org/W203744584","https://openalex.org/W2037111143","https://openalex.org/W2963705282","https://openalex.org/W2283146050","https://openalex.org/W4321149915","https://openalex.org/W2092812142"],"abstract_inverted_index":{"Two":[0],"companion":[1],"algorithms":[2,39,147,175],"are":[3,29,57,106],"developed":[4],"for":[5,17,75,117,152,176],"constructing":[6],"Pade":[7],"fractions":[8,45,155],"along":[9,46,89,156,194],"an":[10,157],"off-diagonal":[11,48,91],"path":[12,159],"of":[13,37,85,97,125,160,168,184],"the":[14,38,41,47,67,86,90,108,126,161,169,182,195],"Pad\u00e9":[15,44,154,162,192],"table":[16],"a":[18,34,83,112,141],"function":[19],"${{":[20],"-":[21],"A(z)}":[22],"/":[23],"{B(z)}}$,":[24],"where":[25],"$A(z)$":[26,54,103],"and":[27,55,95,104],"$B(z)$":[28,56,105],"formal":[30],"power":[31,59],"series":[32,60],"over":[33],"field.":[35],"One":[36],"computes":[40],"first":[42],"n":[43],"in":[49,92],"time":[50],"$O(n^2":[51],")$.":[52],"When":[53,102],"finite":[58],"(i.e.,":[61],"polynomials),":[62],"it":[63,180],"is":[64,69,96,124,167],"shown":[65],"that":[66],"algorithm":[68,74,110,116,123,166],"equivalent":[70],"to":[71,187],"Euclid\u2019s":[72,114],"extended":[73,115],"computing":[76,118,153],"greatest":[77,119,132],"common":[78,120,133],"divisors.":[79,121],"The":[80,122,146,164],"other":[81,130,173],"algorithm,":[82],"generalization":[84],"first,":[87],"proceeds":[88],"quadratic":[93],"steps,":[94],"complexity":[98,128,171],"$O(n\\log":[99],"^2":[100],"n)$.":[101],"polynomials,":[107],"second":[109],"becomes":[111],"fast":[113,131,165,174],"same":[127,170],"as":[129,172],"divisor":[134],"methods,":[135],"but":[136],"its":[137],"iterative":[138],"nature":[139],"provides":[140],"practical":[142],"advantage":[143,183],"during":[144],"implementation.":[145],"may":[148],"also":[149],"be":[150],"used":[151],"anti-diagonal":[158,177],"table.":[163],"computations.":[178],"However,":[179],"has":[181],"being":[185],"able":[186],"determine":[188],"easily":[189],"any":[190],"specific":[191],"fraction":[193],"anti-diagonal.":[196]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}