{"id":"https://openalex.org/W2080901956","doi":"https://doi.org/10.1007/s006070070016","title":"Condition Numbers of Approximate Schur Complements in Two- and Three-Dimensional Discretizations on Hierarchically Ordered Grids","display_name":"Condition Numbers of Approximate Schur Complements in Two- and Three-Dimensional Discretizations on Hierarchically Ordered Grids","publication_year":2000,"publication_date":"2000-11-24","ids":{"openalex":"https://openalex.org/W2080901956","doi":"https://doi.org/10.1007/s006070070016","mag":"2080901956"},"language":"en","primary_location":{"id":"doi:10.1007/s006070070016","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s006070070016","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","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/A5088656822","display_name":"Johannes Kraus","orcid":"https://orcid.org/0000-0003-2261-599X"},"institutions":[{"id":"https://openalex.org/I182712176","display_name":"Montanuniversit\u00e4t Leoben","ror":"https://ror.org/02fhfw393","country_code":"AT","type":"education","lineage":["https://openalex.org/I182712176"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"J. K. Kraus","raw_affiliation_strings":["Department of Applied Mathematics University of Leoben Franz-Josef-Str. 18 A-8700 Leoben Austria e-mail: kraus@unileoben.ac.at, , , , , , AT","Leoben#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics University of Leoben Franz-Josef-Str. 18 A-8700 Leoben Austria e-mail: kraus@unileoben.ac.at, , , , , , AT","institution_ids":["https://openalex.org/I182712176"]},{"raw_affiliation_string":"Leoben#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021127055","display_name":"Clemens Brand","orcid":null},"institutions":[{"id":"https://openalex.org/I182712176","display_name":"Montanuniversit\u00e4t Leoben","ror":"https://ror.org/02fhfw393","country_code":"AT","type":"education","lineage":["https://openalex.org/I182712176"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"C. W. Brand","raw_affiliation_strings":["Department of Applied Mathematics University of Leoben Franz-Josef-Str. 18 A-8700 Leoben Austria e-mail: brand@unileoben.ac.at, , , , , , AT","Leoben#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics University of Leoben Franz-Josef-Str. 18 A-8700 Leoben Austria e-mail: brand@unileoben.ac.at, , , , , , AT","institution_ids":["https://openalex.org/I182712176"]},{"raw_affiliation_string":"Leoben#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18945039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"2","first_page":"135","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9861999750137329,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9714000225067139,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.766069769859314},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.6478425860404968},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6391953825950623},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5913033485412598},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5150275230407715},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.47990286350250244},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4012698233127594},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22325697541236877},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17962750792503357},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15513285994529724},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15200799703598022},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.1260398030281067}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.766069769859314},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.6478425860404968},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6391953825950623},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5913033485412598},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5150275230407715},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.47990286350250244},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4012698233127594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22325697541236877},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17962750792503357},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15513285994529724},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15200799703598022},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.1260398030281067},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s006070070016","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s006070070016","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2277328098","https://openalex.org/W1964968800","https://openalex.org/W1987832651","https://openalex.org/W68723791","https://openalex.org/W1572097765","https://openalex.org/W2024381649","https://openalex.org/W2127652433","https://openalex.org/W2062832849","https://openalex.org/W2950304429","https://openalex.org/W1982468802"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}