{"id":"https://openalex.org/W2048360198","doi":"https://doi.org/10.1137/04060679x","title":"An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems","display_name":"An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2048360198","doi":"https://doi.org/10.1137/04060679x","mag":"2048360198"},"language":"en","primary_location":{"id":"doi:10.1137/04060679x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/04060679x","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/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gene H. Golub","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070728305","display_name":"Chen Greif","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen Greif","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001136231","display_name":"J. M. Varah","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James M. Varah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.012,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.77383699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"3","first_page":"779","last_page":"792"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9973999857902527,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9941999912261963,"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/preconditioner","display_name":"Preconditioner","score":0.9592903852462769},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8446894288063049},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8129955530166626},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6460128426551819},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6270927786827087},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5995446443557739},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5436547994613647},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5412667989730835},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.48397350311279297},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47581177949905396},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.47387954592704773},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45749813318252563},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.42444857954978943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35645127296447754},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33933210372924805},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28322118520736694},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2508987784385681},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22523164749145508},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.18728607892990112},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16094163060188293}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9592903852462769},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8446894288063049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8129955530166626},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6460128426551819},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6270927786827087},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5995446443557739},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5436547994613647},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5412667989730835},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.48397350311279297},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47581177949905396},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.47387954592704773},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45749813318252563},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.42444857954978943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35645127296447754},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33933210372924805},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28322118520736694},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2508987784385681},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22523164749145508},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.18728607892990112},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16094163060188293},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/04060679x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/04060679x","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":19,"referenced_works":["https://openalex.org/W1524324710","https://openalex.org/W1963751327","https://openalex.org/W1981745143","https://openalex.org/W1982604350","https://openalex.org/W1999331305","https://openalex.org/W2003550247","https://openalex.org/W2013737143","https://openalex.org/W2018850201","https://openalex.org/W2049707725","https://openalex.org/W2050206349","https://openalex.org/W2070419067","https://openalex.org/W2077658674","https://openalex.org/W2082727440","https://openalex.org/W2143783905","https://openalex.org/W3016074254","https://openalex.org/W3029645440","https://openalex.org/W4212997115","https://openalex.org/W4243795446","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2401310550","https://openalex.org/W2381322109","https://openalex.org/W1189497506","https://openalex.org/W3146410598","https://openalex.org/W2218557851","https://openalex.org/W1970706285","https://openalex.org/W2767153625","https://openalex.org/W1982069796","https://openalex.org/W2999046577","https://openalex.org/W2986665254"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2],"positive":[3],"definite":[4],"block":[5,20],"preconditioner":[6],"for":[7],"solving":[8],"saddle":[9],"point":[10],"linear":[11],"systems.":[12],"An":[13],"approach":[14],"based":[15],"on":[16],"augmenting":[17],"the":[18,37],"(1,1)":[19],"while":[21],"keeping":[22],"its":[23],"condition":[24],"number":[25],"small":[26],"is":[27,32],"described,":[28],"and":[29,42,44],"algebraic":[30],"analysis":[31],"performed.":[33],"Ways":[34],"of":[35],"selecting":[36],"parameters":[38],"involved":[39],"are":[40,47],"discussed,":[41],"analytical":[43],"numerical":[45],"observations":[46],"given.":[48]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"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":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}