{"id":"https://openalex.org/W2046977198","doi":"https://doi.org/10.1137/040606521","title":"Gaussian Interval Quadrature Formulae for Tchebycheff Systems","display_name":"Gaussian Interval Quadrature Formulae for Tchebycheff Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2046977198","doi":"https://doi.org/10.1137/040606521","mag":"2046977198"},"language":"en","primary_location":{"id":"doi:10.1137/040606521","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040606521","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5088324220","display_name":"Borislav Bojanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borislav Bojanov","raw_affiliation_strings":["Sofia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sofia University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026155157","display_name":"Petar Petrov","orcid":"https://orcid.org/0000-0002-4798-1518"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petar Petrov","raw_affiliation_strings":["Sofia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sofia University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8618,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.74144487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"43","issue":"2","first_page":"787","last_page":"795"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9995999932289124,"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":0.9952999949455261,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8867192268371582},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6937811970710754},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.46983692049980164},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4454708695411682},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.44437921047210693},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39526569843292236},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39258766174316406},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17822852730751038},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.15201503038406372},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.11166515946388245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8867192268371582},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6937811970710754},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.46983692049980164},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4454708695411682},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.44437921047210693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39526569843292236},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39258766174316406},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17822852730751038},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.15201503038406372},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.11166515946388245},{"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040606521","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040606521","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W23656998","https://openalex.org/W73782397","https://openalex.org/W2000883227","https://openalex.org/W2018639632","https://openalex.org/W2031375215","https://openalex.org/W2049660849","https://openalex.org/W2059083646","https://openalex.org/W2085139105","https://openalex.org/W2145289592","https://openalex.org/W4245533130"],"related_works":["https://openalex.org/W2030322846","https://openalex.org/W2042326540","https://openalex.org/W2089411539","https://openalex.org/W2091267724","https://openalex.org/W1973321202","https://openalex.org/W3159111101","https://openalex.org/W1987395535","https://openalex.org/W4210699452","https://openalex.org/W1986739369","https://openalex.org/W2056088350"],"abstract_inverted_index":{"For":[0],"any":[1],"given":[2],"system":[3,14],"of":[4,15,26,40,42,49,52,57],"continuously":[5],"differentiable":[6],"functions":[7],"$\\{u_k\\}_{k=1}^{2n}$":[8],"that":[9],"constitute":[10],"an":[11,47],"extended":[12],"Tchebycheff":[13],"order":[16],"2":[17],"on":[18,33],"[a,b]":[19,41],"we":[20],"prove":[21],"the":[22,27,50],"existence":[23],"and":[24],"uniqueness":[25],"Gaussian":[28],"interval":[29],"quadrature":[30],"formula":[31],"based":[32],"n":[34],"weighted":[35],"integrals":[36],"over":[37],"nonoverlapping":[38],"subintervals":[39],"preassigned":[43],"lengths.":[44],"This":[45],"supplies":[46],"analogue":[48],"result":[51],"Krein":[53],"about":[54],"canonical":[55],"representation":[56],"linear":[58],"positive":[59],"functionals.":[60]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}