{"id":"https://openalex.org/W4407277127","doi":"https://doi.org/10.1007/s11075-025-02021-z","title":"On computing the zeros of Laguerre\u2013Sobolev polynomials","display_name":"On computing the zeros of Laguerre\u2013Sobolev polynomials","publication_year":2025,"publication_date":"2025-02-08","ids":{"openalex":"https://openalex.org/W4407277127","doi":"https://doi.org/10.1007/s11075-025-02021-z"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-025-02021-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-025-02021-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02021-z.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02021-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002510034","display_name":"Teresa Laudadio","orcid":"https://orcid.org/0000-0002-2046-0456"},"institutions":[{"id":"https://openalex.org/I4210106125","display_name":"Istituto per le Applicazioni del Calcolo Mauro Picone","ror":"https://ror.org/00ygy3d85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210106125","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"T. Laudadio","raw_affiliation_strings":["Istituto per le Applicazioni del Calcolo \u201cM. Picone\u201d, Consiglio Nazionale delle Ricerche, via Amendola 122/D, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto per le Applicazioni del Calcolo \u201cM. Picone\u201d, Consiglio Nazionale delle Ricerche, via Amendola 122/D, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036811999","display_name":"Nicola Mastronardi","orcid":"https://orcid.org/0000-0002-0045-2862"},"institutions":[{"id":"https://openalex.org/I4210106125","display_name":"Istituto per le Applicazioni del Calcolo Mauro Picone","ror":"https://ror.org/00ygy3d85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210106125","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"N. Mastronardi","raw_affiliation_strings":["Istituto per le Applicazioni del Calcolo \u201cM. Picone\u201d, Consiglio Nazionale delle Ricerche, via Amendola 122/D, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto per le Applicazioni del Calcolo \u201cM. Picone\u201d, Consiglio Nazionale delle Ricerche, via Amendola 122/D, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024913306","display_name":"Francisco Jos\u00e9 Marcell\u00e1n Espa\u00f1ol","orcid":null},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"F. J. Marcell\u00e1n Espa\u00f1ol","raw_affiliation_strings":["Department of Mathematics, University Carlos III de Madrid, Avenida de la Universidad, 30, Legan\u00e9s, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Carlos III de Madrid, Avenida de la Universidad, 30, Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014426766","display_name":"Niel Van Buggenhout","orcid":"https://orcid.org/0000-0003-0856-0670"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"N. Van Buggenhout","raw_affiliation_strings":["Department of Mathematics, University Carlos III de Madrid, Avenida de la Universidad, 30, Legan\u00e9s, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Carlos III de Madrid, Avenida de la Universidad, 30, Legan\u00e9s, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036923077","display_name":"Paul Van Dooren","orcid":"https://orcid.org/0000-0002-0115-9932"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P. Van Dooren","raw_affiliation_strings":["Department of Mathematical Engineering, Catholic University of Louvain, Avenue Georges Lemaitre 4, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Catholic University of Louvain, Avenue Georges Lemaitre 4, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5002510034"],"corresponding_institution_ids":["https://openalex.org/I4210106125"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":13.5586,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.98651392,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"100","issue":"4","first_page":"1507","last_page":"1526"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9994000196456909,"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":0.9994000196456909,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laguerre-polynomials","display_name":"Laguerre polynomials","score":0.859086811542511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8507646918296814},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6948484778404236},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6622267365455627},{"id":"https://openalex.org/keywords/laguerres-method","display_name":"Laguerre's method","score":0.5117127895355225},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.3888978958129883},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.3868715763092041},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36762717366218567},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34397006034851074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10302498936653137}],"concepts":[{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.859086811542511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8507646918296814},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6948484778404236},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6622267365455627},{"id":"https://openalex.org/C43475892","wikidata":"https://www.wikidata.org/wiki/Q1171964","display_name":"Laguerre's method","level":4,"score":0.5117127895355225},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.3888978958129883},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.3868715763092041},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36762717366218567},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34397006034851074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10302498936653137}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-025-02021-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-025-02021-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02021-z.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-025-02021-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-025-02021-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02021-z.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3131047749","display_name":null,"funder_award_id":"20227PCCK","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3429648993","display_name":null,"funder_award_id":"PID202","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4126322094","display_name":null,"funder_award_id":"01100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G439775126","display_name":null,"funder_award_id":"20227PCCKZ","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G661330594","display_name":null,"funder_award_id":"00110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6685425346","display_name":null,"funder_award_id":"0011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8497050386","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320322651","display_name":"Consiglio Nazionale delle Ricerche","ror":"https://ror.org/04zaypm56"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407277127.pdf","grobid_xml":"https://content.openalex.org/works/W4407277127.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W177090654","https://openalex.org/W1966268321","https://openalex.org/W2005988701","https://openalex.org/W2020328455","https://openalex.org/W2025026078","https://openalex.org/W2040286684","https://openalex.org/W2042255949","https://openalex.org/W2046133214","https://openalex.org/W2058689772","https://openalex.org/W2083781733","https://openalex.org/W2095409933","https://openalex.org/W2117948699","https://openalex.org/W2156010245","https://openalex.org/W2490807609","https://openalex.org/W2783213324","https://openalex.org/W2800664160","https://openalex.org/W2935959741","https://openalex.org/W4246797080","https://openalex.org/W4312258136","https://openalex.org/W4385543582","https://openalex.org/W4388084951","https://openalex.org/W4393275928","https://openalex.org/W4399794998","https://openalex.org/W4400111776","https://openalex.org/W4402312407","https://openalex.org/W4405838688"],"related_works":["https://openalex.org/W4253809742","https://openalex.org/W1981317805","https://openalex.org/W2067193525","https://openalex.org/W4312412686","https://openalex.org/W3102828547","https://openalex.org/W4391069448","https://openalex.org/W4245614420","https://openalex.org/W2599548904","https://openalex.org/W2353888022","https://openalex.org/W1997701590"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,30],"work,":[3],"we":[4,89,109],"focus":[5],"on":[6],"the":[7,10,25,56,77,82,98,101,104,151,154],"computation":[8],"of":[9,12,18,51,100,103,153],"zeros":[11],"a":[13,36,41,46,91,111],"monic":[14],"Laguerre\u2013Sobolev":[15],"orthogonal":[16],"polynomial":[17],"degree":[19],"n":[20,53],".":[21,54],"Taking":[22],"into":[23],"account":[24],"associated":[26],"four\u2013term":[27],"recurrence":[28],"relation,":[29],"problem":[31,60],"can":[32],"be":[33],"formulated":[34],"as":[35],"generalized":[37,58,78],"eigenvalue":[38,59,79],"problem,":[39,80],"involving":[40],"lower":[42,48],"bidiagonal":[43],"matrix":[44,50,106,156],"and":[45,64,113,135],"2\u2013banded":[47],"Hessenberg":[49],"order":[52],"Unfortunately,":[55],"considered":[57,155],"is":[61],"very":[62],"ill\u2013conditioned,":[63],"classical":[65],"balancing":[66,93],"procedures":[67],"do":[68],"not":[69],"improve":[70],"it.":[71],"Therefore,":[72],"customary":[73],"techniques":[74],"for":[75],"solving":[76],"like":[81],"QZ":[83],"method,":[84],"yield":[85],"unreliable":[86],"results.":[87],"Here,":[88],"propose":[90,110],"novel":[92],"procedure":[94],"that":[95],"drastically":[96],"reduces":[97],"ill\u2013conditioning":[99],"eigenvalues":[102],"involved":[105],"pencil.":[107,157],"Moreover,":[108],"fast":[112],"reliable":[114],"algorithm,":[115],"with":[116],"$$":[117,120,136,139],"\\mathcal":[118,137],"{O}(n^2)":[119],"<mml:math":[121,140],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[122,141],"<mml:mrow>":[123,142],"<mml:mi>O</mml:mi>":[124,143],"<mml:mo>(</mml:mo>":[125,144],"<mml:msup>":[126],"<mml:mi>n</mml:mi>":[127,145],"<mml:mn>2</mml:mn>":[128],"</mml:msup>":[129],"<mml:mo>)</mml:mo>":[130,146],"</mml:mrow>":[131,147],"</mml:math>":[132,148],"computational":[133],"complexity":[134],"{O}(n)":[138],"memory,":[149],"exploiting":[150],"structure":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}