{"id":"https://openalex.org/W7225707887","doi":"https://doi.org/10.37394/23203.2026.21.45","title":"Pad\u00e9 Approximants via Matrix Elementary Row Operations: Algorithm, Error Bounds, and Optimality","display_name":"Pad\u00e9 Approximants via Matrix Elementary Row Operations: Algorithm, Error Bounds, and Optimality","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225707887","doi":"https://doi.org/10.37394/23203.2026.21.45"},"language":"en","primary_location":{"id":"doi:10.37394/23203.2026.21.45","doi":"https://doi.org/10.37394/23203.2026.21.45","is_oa":true,"landing_page_url":"https://doi.org/10.37394/23203.2026.21.45","pdf_url":"https://wseas.com/journals/sac/2026/a905106-2407.pdf","source":{"id":"https://openalex.org/S4210175621","display_name":"WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL","issn_l":"1991-8763","issn":["1991-8763","2224-2856"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320666","host_organization_name":"World Scientific and Engineering Academy and Society","host_organization_lineage":["https://openalex.org/P4310320666"],"host_organization_lineage_names":["World Scientific and Engineering Academy and Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"WSEAS Transactions on Systems and Control","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://wseas.com/journals/sac/2026/a905106-2407.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003124357","display_name":"Wannatida Yonwilad","orcid":"https://orcid.org/0000-0002-0028-829X","observed_orcids":["https://orcid.org/0000-0002-0028-829X","https://orcid.org/0000-0002-8469-9642"]},"institutions":[{"id":"https://openalex.org/I4210130206","display_name":"Kalasin University","ror":"https://ror.org/02g702008","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210130206"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Wannatida Yonwilad","raw_affiliation_strings":["Department of Learning Management Innovation, Faculty of Education and Educational Innovation, Kalasin University, Kalasin 46230, THAILAND"],"raw_orcid":"https://orcid.org/0000-0002-0028-829X","affiliations":[{"raw_affiliation_string":"Department of Learning Management Innovation, Faculty of Education and Educational Innovation, Kalasin University, Kalasin 46230, THAILAND","institution_ids":["https://openalex.org/I4210130206"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5144313077","display_name":"Ekkawit Lampai","orcid":"https://orcid.org/0009-0006-8462-7776","observed_orcids":["https://orcid.org/0009-0006-8462-7776"]},"institutions":[{"id":"https://openalex.org/I4210135781","display_name":"Rajabhat Maha Sarakham University","ror":"https://ror.org/03n273w86","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210135781"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Ekkawit Lampai","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Rajabhat Maha Sarakham University, Maha Sarakham 44000, THAILAND"],"raw_orcid":"https://orcid.org/0009-0006-8462-7776","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Rajabhat Maha Sarakham University, Maha Sarakham 44000, THAILAND","institution_ids":["https://openalex.org/I4210135781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":null,"first_page":"523","last_page":"523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9413999915122986,"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":0.9413999915122986,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.023800000548362732,"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/T11081","display_name":"Advanced Control Systems Design","score":0.02319999970495701,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pade-approximants","display_name":"Pad\u00e9 approximants","score":0.9990000128746033},{"id":"https://openalex.org/keywords/augmented-matrix","display_name":"augmented matrix","score":0.5580000281333923},{"id":"https://openalex.org/keywords/formal-power-series","display_name":"formal power series","score":0.781000018119812},{"id":"https://openalex.org/keywords/determinant-criterion","display_name":"determinant criterion","score":0.8059999942779541},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.7820000052452087},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.9750000238418579}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7960000038146973},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7275000214576721},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5667999982833862},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5648999810218811},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.531000018119812},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5184000134468079},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46219998598098755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3682999908924103},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.35659998655319214},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.34709998965263367},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3215999901294708},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.29159998893737793},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.25839999318122864}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37394/23203.2026.21.45","doi":"https://doi.org/10.37394/23203.2026.21.45","is_oa":true,"landing_page_url":"https://doi.org/10.37394/23203.2026.21.45","pdf_url":"https://wseas.com/journals/sac/2026/a905106-2407.pdf","source":{"id":"https://openalex.org/S4210175621","display_name":"WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL","issn_l":"1991-8763","issn":["1991-8763","2224-2856"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320666","host_organization_name":"World Scientific and Engineering Academy and Society","host_organization_lineage":["https://openalex.org/P4310320666"],"host_organization_lineage_names":["World Scientific and Engineering Academy and Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"WSEAS Transactions on Systems and Control","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37394/23203.2026.21.45","doi":"https://doi.org/10.37394/23203.2026.21.45","is_oa":true,"landing_page_url":"https://doi.org/10.37394/23203.2026.21.45","pdf_url":"https://wseas.com/journals/sac/2026/a905106-2407.pdf","source":{"id":"https://openalex.org/S4210175621","display_name":"WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL","issn_l":"1991-8763","issn":["1991-8763","2224-2856"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320666","host_organization_name":"World Scientific and Engineering Academy and Society","host_organization_lineage":["https://openalex.org/P4310320666"],"host_organization_lineage_names":["World Scientific and Engineering Academy and Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"WSEAS Transactions on Systems and Control","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225707887.pdf","grobid_xml":"https://content.openalex.org/works/W7225707887.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W351274383","https://openalex.org/W2000583785","https://openalex.org/W2006908379","https://openalex.org/W2009394335","https://openalex.org/W2020804487","https://openalex.org/W2106565812","https://openalex.org/W2120516507","https://openalex.org/W2122766764","https://openalex.org/W2130956934","https://openalex.org/W2156464932","https://openalex.org/W2156523753","https://openalex.org/W2312964503","https://openalex.org/W2498647973","https://openalex.org/W2560261741","https://openalex.org/W2728482692","https://openalex.org/W3080914972","https://openalex.org/W4233501930","https://openalex.org/W4303083268","https://openalex.org/W4416949965","https://openalex.org/W7163921900","https://openalex.org/W7172426818"],"related_works":["https://openalex.org/W4213206185","https://openalex.org/W2004837356","https://openalex.org/W2279239614","https://openalex.org/W2040035683","https://openalex.org/W7172426818","https://openalex.org/W2080136153","https://openalex.org/W2122766764","https://openalex.org/W2765744254","https://openalex.org/W2525277292","https://openalex.org/W7099504117"],"abstract_inverted_index":{"We":[0,156],"develop":[1],"a":[2,35,48,67,70,93,115,146,159,170,186],"matrix":[3],"elementary":[4],"row":[5],"operations":[6],"(ERO)":[7],"framework":[8],"for":[9],"computing":[10],"Pad\u00e9":[11,25,83,164,179],"approximants":[12],"and":[13,47,87,136,169],"analyzing":[14],"their":[15],"accuracy,":[16],"extending":[17],"an":[18,43,88,122,166],"integer":[19],"augmented-matrix":[20],"device":[21],"to":[22],"the":[23,54,75,82,163,178,182],"whole":[24],"table.":[26],"The":[27,117],"[":[28],"m":[29,78],"/":[30,106,144],"n":[31,80,101,103,109,110,132,134,141,150],"]":[32],"approximant":[33],"of":[34,81,114,162],"formal":[36],"power":[37],"series":[38],"is":[39,85,112],"obtained":[40],"by":[41],"row-reducing":[42],"augmented":[44],"Pad\u00e9\u2013Sylvester":[45],"matrix,":[46],"determinant":[49],"criterion":[50],"certifies":[51],"nondegeneracy.":[52],"For":[53,174],"exponential":[55],"learning":[56],"function":[57],"L":[58],"(":[59,107,139,145],"t":[60,68,147,152],")":[61,111,142,148],"=":[62,104],"1":[63,105],"\u2212":[64,66],"e":[65],",":[69,102,133,135],"transfer":[71],"lemma":[72],"proves":[73],"that":[74],"lower":[76],"triangle":[77],"\u2265":[79],"table":[84],"nondegenerate,":[86],"exact":[89,123,183],"Beta-integral":[90],"remainder":[91],"gives":[92],"uniform":[94],"error":[95,119],"bound":[96],"whose":[97],"diagonal":[98],"constant":[99],"K":[100,131],"2":[108,140,149],"independent":[113],".":[116,155],"Pad\u00e9-to-Taylor":[118],"ratio":[120],"has":[121],"quotient-of-integrals":[124],"representation;":[125],"it":[126],"decreases":[127],"strictly,":[128],"stays":[129],"below":[130],"behaves":[137],"like":[138],"!":[143],"as":[151],"\u2192":[153],"\u221e":[154],"also":[157],"give":[158],"shape":[160],"analysis":[161],"curve,":[165],"order-selection":[167],"theorem,":[168],"numerical":[171],"stability":[172],"study.":[173],"optimal":[175],"time":[176],"allocation,":[177],"surrogate":[180],"recovers":[181],"optimum":[184],"within":[185],"certified":[187],"bound.":[188]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-11T00:00:00"}