{"id":"https://openalex.org/W2053315218","doi":"https://doi.org/10.1137/s0895479892236933","title":"Algebraic Analysis of the Hierarchical Basis Preconditioner","display_name":"Algebraic Analysis of the Hierarchical Basis Preconditioner","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2053315218","doi":"https://doi.org/10.1137/s0895479892236933","mag":"2053315218"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479892236933","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479892236933","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/A5086424147","display_name":"Howard C. Elman","orcid":"https://orcid.org/0000-0002-8886-9901"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Howard C. Elman","raw_affiliation_strings":["University of Maryland, College Park"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100336509","display_name":"Xuejun Zhang","orcid":"https://orcid.org/0000-0002-6268-7309"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xuejun Zhang","raw_affiliation_strings":["University of Maryland, College Park"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5448,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.66164914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"1","first_page":"192","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9948999881744385,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8599376678466797},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7753254771232605},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6615753173828125},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5611131191253662},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5337904691696167},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4920737147331238},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.48288941383361816},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4811474084854126},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4698791801929474},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4692152738571167},{"id":"https://openalex.org/keywords/algebraic-analysis","display_name":"Algebraic analysis","score":0.44573473930358887},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43594327569007874},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3579542636871338},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29690805077552795},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2690344452857971},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.18127819895744324},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.16533198952674866},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09363937377929688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8599376678466797},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7753254771232605},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6615753173828125},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5611131191253662},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5337904691696167},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4920737147331238},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.48288941383361816},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4811474084854126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4698791801929474},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4692152738571167},{"id":"https://openalex.org/C554573382","wikidata":"https://www.wikidata.org/wiki/Q4723988","display_name":"Algebraic analysis","level":5,"score":0.44573473930358887},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43594327569007874},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3579542636871338},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29690805077552795},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2690344452857971},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.18127819895744324},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.16533198952674866},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09363937377929688}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479892236933","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479892236933","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W256654499","https://openalex.org/W1493981498","https://openalex.org/W1496738390","https://openalex.org/W2018685527","https://openalex.org/W2041308917","https://openalex.org/W2044355921","https://openalex.org/W2060170348","https://openalex.org/W2090589476","https://openalex.org/W2321310861","https://openalex.org/W2568618671","https://openalex.org/W3147515309","https://openalex.org/W4238784554"],"related_works":["https://openalex.org/W2357336958","https://openalex.org/W4281839678","https://openalex.org/W2535797495","https://openalex.org/W152950973","https://openalex.org/W2300963337","https://openalex.org/W2283235658","https://openalex.org/W3162287216","https://openalex.org/W2058487055","https://openalex.org/W2025305727","https://openalex.org/W4288024367"],"abstract_inverted_index":{"The":[0],"use":[1],"of":[2,10,21,31],"the":[3,49],"hierarchical":[4],"basis":[5],"in":[6,37],"finite":[7],"element":[8],"discretizations":[9],"two-dimensional":[11],"elliptic":[12],"partial":[13],"differential":[14],"equations":[15],"produces":[16],"matrices":[17],"with":[18],"condition":[19],"numbers":[20],"order":[22],"$O((\\log":[23],"h^{":[24],"-":[25],"1}":[26],")^2":[27],")$.":[28],"Standard":[29],"proofs":[30],"this":[32,40],"result":[33,50],"are":[34],"functional":[35],"analytic":[36],"style.":[38],"In":[39],"paper,":[41],"it":[42],"is":[43],"shown":[44],"that":[45],"for":[46],"uniform":[47],"grids":[48],"can":[51],"be":[52],"obtained":[53],"using":[54],"a":[55],"purely":[56],"linear":[57],"algebraic":[58],"argument.":[59]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}