{"id":"https://openalex.org/W4385780620","doi":"https://doi.org/10.1002/nla.2527","title":"Accurate bidiagonal decomposition of Lagrange\u2013Vandermonde matrices and applications","display_name":"Accurate bidiagonal decomposition of Lagrange\u2013Vandermonde matrices and applications","publication_year":2023,"publication_date":"2023-08-12","ids":{"openalex":"https://openalex.org/W4385780620","doi":"https://doi.org/10.1002/nla.2527"},"language":"en","primary_location":{"id":"doi:10.1002/nla.2527","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2527","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2527","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2527","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080907582","display_name":"Ana Marco","orcid":"https://orcid.org/0000-0003-4662-6327"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Ana Marco","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas Universidad de Alcal\u00e1  Alcal\u00e1 de Henares Spain"],"raw_orcid":"https://orcid.org/0000-0003-4662-6327","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas Universidad de Alcal\u00e1  Alcal\u00e1 de Henares Spain","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052327276","display_name":"Jos\u00e9\u2010Javier Mart\u00ednez","orcid":"https://orcid.org/0000-0002-8322-0361"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9\u2010Javier Mart\u00ednez","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas Universidad de Alcal\u00e1  Alcal\u00e1 de Henares Spain"],"raw_orcid":"https://orcid.org/0000-0002-8322-0361","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas Universidad de Alcal\u00e1  Alcal\u00e1 de Henares Spain","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030840239","display_name":"Raquel Via\u00f1a","orcid":"https://orcid.org/0000-0001-5484-9104"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Raquel Via\u00f1a","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas Universidad de Alcal\u00e1  Alcal\u00e1 de Henares Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas Universidad de Alcal\u00e1  Alcal\u00e1 de Henares Spain","institution_ids":["https://openalex.org/I189268942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080907582"],"corresponding_institution_ids":["https://openalex.org/I189268942"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":{"value":4430,"currency":"USD","value_usd":4430},"fwci":0.6909,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73680138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"31","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.947418212890625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.784835159778595},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6669203639030457},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.6355007886886597},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5862647294998169},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5660454630851746},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5565987229347229},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5381072759628296},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5194017887115479},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.44831493496894836},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4251982271671295},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35488444566726685},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28897398710250854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23988208174705505},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21930909156799316},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18999570608139038},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11866387724876404},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1098448634147644},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.05815237760543823}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.947418212890625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.784835159778595},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6669203639030457},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.6355007886886597},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5862647294998169},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5660454630851746},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5565987229347229},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5381072759628296},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5194017887115479},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.44831493496894836},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4251982271671295},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35488444566726685},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28897398710250854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23988208174705505},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21930909156799316},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18999570608139038},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11866387724876404},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1098448634147644},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.05815237760543823},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/nla.2527","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2527","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2527","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:ebuah.uah.es:10017/63570","is_oa":true,"landing_page_url":"http://hdl.handle.net/10017/63570","pdf_url":"https://ebuah.uah.es/dspace/bitstream/10017/63570/3/Accurate_Marco_NumLinAlgApp_2024.pdf","source":{"id":"https://openalex.org/S7407055200","display_name":"e_Buah","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1002/nla.2527","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2527","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2527","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323755","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385780620.pdf","grobid_xml":"https://content.openalex.org/works/W4385780620.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W50638871","https://openalex.org/W565573710","https://openalex.org/W1981115560","https://openalex.org/W1988043369","https://openalex.org/W1989660476","https://openalex.org/W2054956151","https://openalex.org/W2060452389","https://openalex.org/W2094302535","https://openalex.org/W2100510181","https://openalex.org/W2156792823","https://openalex.org/W2158200065","https://openalex.org/W2481174673","https://openalex.org/W2560684249","https://openalex.org/W2581875623","https://openalex.org/W2899195779","https://openalex.org/W3098068395","https://openalex.org/W3106727077","https://openalex.org/W3128736037","https://openalex.org/W4200068082","https://openalex.org/W4283326178","https://openalex.org/W4293062468","https://openalex.org/W4299822471"],"related_works":["https://openalex.org/W3046922746","https://openalex.org/W3161838140","https://openalex.org/W1648644969","https://openalex.org/W3003354345","https://openalex.org/W3092940009","https://openalex.org/W2364141700","https://openalex.org/W2125621309","https://openalex.org/W4385780620","https://openalex.org/W4300463889","https://openalex.org/W2962769476"],"abstract_inverted_index":{"Abstract":[0],"Lagrange\u2013Vandermonde":[1],"matrices":[2,6,45,60,115,118,128],"are":[3,41,46,81,116,129,142],"the":[4,14,28,33,37,55,70,95,109,113,121,136],"collocation":[5,39,117,127],"corresponding":[7,38,119],"to":[8,31,53,61,99,103,120],"Lagrange\u2010type":[9,34],"bases,":[10],"obtained":[11],"by":[12],"removing":[13],"denominators":[15],"from":[16],"each":[17],"element":[18],"of":[19,58,72,92,108,139],"a":[20],"Lagrange":[21,123],"basis.":[22],"It":[23],"is":[24,65],"proved":[25],"that,":[26],"provided":[27],"nodes":[29],"required":[30],"create":[32],"basis":[35],"and":[36,78,86,102],"matrix":[40],"properly":[42],"ordered,":[43],"such":[44,126],"strictly":[47],"totally":[48,131],"positive.":[49,132],"A":[50],"fast":[51],"algorithm":[52],"compute":[54],"bidiagonal":[56],"decomposition":[57],"these":[59],"high":[62,104],"relative":[63,105],"accuracy":[64,106],"presented.":[66],"As":[67],"an":[68,84],"application,":[69],"problems":[71,111],"eigenvalue":[73],"computation,":[74],"linear":[75],"system":[76],"solving":[77],"inverse":[79],"computation":[80],"solved":[82],"in":[83],"efficient":[85],"accurate":[87],"way":[88],"for":[89],"this":[90],"type":[91],"matrices.":[93],"Moreover,":[94],"proposed":[96],"algorithms":[97],"allow":[98],"solve":[100],"fastly":[101],"some":[107],"cited":[110],"when":[112],"involved":[114],"standard":[122],"basis,":[124],"although":[125],"not":[130],"Numerical":[133],"experiments":[134],"illustrating":[135],"good":[137],"performance":[138],"our":[140],"approach":[141],"also":[143],"included.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}