{"id":"https://openalex.org/W4399089802","doi":"https://doi.org/10.1007/s11786-024-00581-2","title":"A Low-Rank Matrix Approach to Compute Polynomial Approximations of Smooth Two-Dimensional Functions","display_name":"A Low-Rank Matrix Approach to Compute Polynomial Approximations of Smooth Two-Dimensional Functions","publication_year":2024,"publication_date":"2024-05-28","ids":{"openalex":"https://openalex.org/W4399089802","doi":"https://doi.org/10.1007/s11786-024-00581-2"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-024-00581-2","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11786-024-00581-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-024-00581-2.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","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/s11786-024-00581-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102674548","display_name":"Nilson J. Lima","orcid":null},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Nilson J. Lima","raw_affiliation_strings":["CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre s/n, Porto, 4169-007, Portugal"],"affiliations":[{"raw_affiliation_string":"CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre s/n, Porto, 4169-007, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003819222","display_name":"Jos\u00e9 A. O. Matos","orcid":"https://orcid.org/0000-0003-0570-7913"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 A. O. Matos","raw_affiliation_strings":["CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias s/n, Porto, 4200-464, Portugal"],"affiliations":[{"raw_affiliation_string":"CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias s/n, Porto, 4200-464, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039423894","display_name":"Paulo B. Vasconcelos","orcid":"https://orcid.org/0000-0002-7132-880X"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Paulo B. Vasconcelos","raw_affiliation_strings":["CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias s/n, Porto, 4200-464, Portugal"],"affiliations":[{"raw_affiliation_string":"CMUP, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias s/n, Porto, 4200-464, Portugal","institution_ids":["https://openalex.org/I182534213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102674548"],"corresponding_institution_ids":["https://openalex.org/I182534213"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3602,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57169782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9980000257492065,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/low-rank-approximation","display_name":"Low-rank approximation","score":0.7064359188079834},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6606332659721375},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.651005208492279},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5897987484931946},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5649900436401367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5441833138465881},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5183976292610168},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5098739862442017},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4854715168476105},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.45027559995651245},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4345114529132843},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4217427670955658},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4115600287914276},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3592306971549988},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3568475544452667},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3128173351287842},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20031052827835083},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16516277194023132},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.10216149687767029},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10086795687675476}],"concepts":[{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.7064359188079834},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6606332659721375},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.651005208492279},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5897987484931946},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5649900436401367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5441833138465881},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5183976292610168},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5098739862442017},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4854715168476105},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.45027559995651245},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4345114529132843},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4217427670955658},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4115600287914276},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3592306971549988},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3568475544452667},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3128173351287842},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20031052827835083},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16516277194023132},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.10216149687767029},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10086795687675476},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.0},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11786-024-00581-2","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11786-024-00581-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-024-00581-2.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11786-024-00581-2","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11786-024-00581-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-024-00581-2.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324086","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399089802.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2025485823","https://openalex.org/W2040187556","https://openalex.org/W2079598795","https://openalex.org/W2167965189","https://openalex.org/W2962986325","https://openalex.org/W2963450965","https://openalex.org/W3035965352","https://openalex.org/W3099878876","https://openalex.org/W4238447884","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W2010100052","https://openalex.org/W2148568324","https://openalex.org/W1990844505","https://openalex.org/W1607100495","https://openalex.org/W4378770618","https://openalex.org/W4386721910","https://openalex.org/W4094001","https://openalex.org/W2163255469"],"abstract_inverted_index":{"Abstract":[0],"Polynomial":[1],"approximation":[2,75],"of":[3,76,84],"smooth":[4,78,86],"functions":[5,79,87],"is":[6],"becoming":[7],"increasingly":[8],"important":[9],"in":[10,22],"fields":[11],"like":[12],"numerical":[13],"analysis":[14],"and":[15,57,83],"scientific":[16],"computing.":[17],"These":[18,95],"approximations":[19],"are":[20,97],"vital":[21],"models":[23],"that":[24],"rely":[25],"on":[26,50,72],"spectral":[27,111],"methods.":[28],"To":[29],"reduce":[30],"the":[31,73,81,93,110],"memory":[32],"costs":[33],"for":[34,105],"large":[35],"dimensional":[36],"problems,":[37],"various":[38],"methods":[39,48],"to":[40,63],"provide":[41],"data-sparse":[42],"representations":[43],"have":[44],"been":[45],"proposed,":[46],"including":[47],"based":[49],"singular":[51],"value":[52],"decomposition,":[53],"adaptive":[54],"cross":[55],"approximation,":[56],"matrices":[58],"with":[59],"hierarchical":[60],"low-rank":[61,89],"structures,":[62],"mention":[64],"a":[65,101],"few.":[66],"This":[67],"work":[68],"presents":[69],"implementation":[70],"details":[71],"polynomial":[74],"univariate":[77],"through":[80],"class,":[82],"bivariate":[85],"by":[88,109],"matrix":[90],"representation":[91],"via":[92],"class.":[94],"approaches":[96],"explained":[98],"within":[99],",":[100],"mathematical":[102],"software":[103],"library":[104],"solving":[106],"integro-differential":[107],"problems":[108],"Tau":[112],"method.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2025-10-10T00:00:00"}
