{"id":"https://openalex.org/W1967535604","doi":"https://doi.org/10.1137/s0895479803423822","title":"Quadrature Rules Based on the Arnoldi Process","display_name":"Quadrature Rules Based on the Arnoldi Process","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1967535604","doi":"https://doi.org/10.1137/s0895479803423822","mag":"1967535604"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479803423822","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803423822","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5090411877","display_name":"Daniela Calvetti","orcid":"https://orcid.org/0000-0001-5696-718X"},"institutions":[{"id":"https://openalex.org/I58956616","display_name":"Case Western Reserve University","ror":"https://ror.org/051fd9666","country_code":"US","type":"education","lineage":["https://openalex.org/I58956616"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniela Calvetti","raw_affiliation_strings":["Case Western Reserve University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Case Western Reserve University ,","institution_ids":["https://openalex.org/I58956616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742470","display_name":"Sunmi Kim","orcid":"https://orcid.org/0000-0001-7475-7274"},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sun-Mi Kim","raw_affiliation_strings":["Kent State Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kent State Univ","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072817181","display_name":"Lothar Reichel","orcid":"https://orcid.org/0000-0003-1729-6816"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lothar Reichel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3493,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.80531526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"3","first_page":"765","last_page":"781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9986000061035156,"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/T12504","display_name":"Mathematics and Applications","score":0.9907000064849854,"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/mathematics","display_name":"Mathematics","score":0.7704943418502808},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.7369019389152527},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7241939306259155},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6324737071990967},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5918170213699341},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5396751165390015},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4911003112792969},{"id":"https://openalex.org/keywords/quadratic-form","display_name":"Quadratic form (statistics)","score":0.4365263283252716},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35885167121887207},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24337908625602722},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17185917496681213},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05642533302307129}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7704943418502808},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.7369019389152527},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7241939306259155},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6324737071990967},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5918170213699341},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5396751165390015},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4911003112792969},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.4365263283252716},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35885167121887207},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24337908625602722},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17185917496681213},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05642533302307129},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479803423822","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803423822","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W21724089","https://openalex.org/W26707179","https://openalex.org/W185370267","https://openalex.org/W199485284","https://openalex.org/W1484739396","https://openalex.org/W1490898760","https://openalex.org/W1506342804","https://openalex.org/W1570537360","https://openalex.org/W1630543171","https://openalex.org/W1980461259","https://openalex.org/W1981745143","https://openalex.org/W1984347942","https://openalex.org/W1987841088","https://openalex.org/W2006340475","https://openalex.org/W2089310106","https://openalex.org/W2128978199","https://openalex.org/W2798909945","https://openalex.org/W2990667227","https://openalex.org/W4213416190","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1638654081","https://openalex.org/W4255530064","https://openalex.org/W4252367085","https://openalex.org/W4301465988","https://openalex.org/W2128141353","https://openalex.org/W2047406140","https://openalex.org/W4289097017","https://openalex.org/W2352916597","https://openalex.org/W2043832110","https://openalex.org/W2906702131"],"abstract_inverted_index":{"Applying":[0],"a":[1,9],"few":[2],"steps":[3],"of":[4,26,37,40,81],"the":[5,35,41,61,66,70,73,82],"Arnoldi":[6],"process":[7],"to":[8,20,34],"large":[10],"nonsymmetric":[11],"matrix":[12,67],"A":[13],"with":[14],"initial":[15],"vector":[16,71],"v":[17],"is":[18,55],"shown":[19],"induce":[21],"several":[22],"quadrature":[23],"rules.":[24],"Properties":[25],"these":[27],"rules":[28],"are":[29],"discussed,":[30],"and":[31,49,52,64,69,78,84],"their":[32],"application":[33],"computation":[36],"inexpensive":[38],"estimates":[39,75],"quadratic":[42,51,83],"form":[43],"<f,g>":[44],":=":[45],"v*":[46],"(f(A))*g":[47],"(A)v":[48],"related":[50],"bilinear":[53,85],"forms":[54],"considered.":[56],"Under":[57],"suitable":[58],"conditions":[59],"on":[60],"functions":[62],"f":[63],"g,":[65],"A,":[68],"v,":[72],"computed":[74],"provide":[76],"upper":[77],"lower":[79],"bounds":[80],"forms.":[86]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"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"}
