{"id":"https://openalex.org/W1603096017","doi":"https://doi.org/10.1137/040618680","title":"A class of nonsymmetric preconditioners for saddle point problems","display_name":"A class of nonsymmetric preconditioners for saddle point problems","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1603096017","doi":"https://doi.org/10.1137/040618680","mag":"1603096017"},"language":"en","primary_location":{"id":"pmh:oai:ris.utwente.nl:openaire/3646a431-5bf4-47e8-a285-1c042c41fbde","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/3646a431-5bf4-47e8-a285-1c042c41fbde","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bochev, M A & Golub, G H 2006, 'A Class of Nonsymmetric Preconditioners for Saddle Point Problems', SIAM journal on matrix analysis and applications, vol. 27, no. Technical/4, 10.1137/040618680, pp. 1125-1149. https://doi.org/10.1137/040618680","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"report","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.utwente.nl/en/publications/3646a431-5bf4-47e8-a285-1c042c41fbde","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014581389","display_name":"Mikhail A. Bochev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bochev, Mikhail A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Golub, G.H.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Golub, G.H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9595000147819519,"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":0.9595000147819519,"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/T12303","display_name":"Tensor decomposition and applications","score":0.011300000362098217,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.005499999970197678,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7057355046272278},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6301282644271851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5866632461547852},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4996061325073242},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.46233177185058594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45140019059181213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37941253185272217},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.29752397537231445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29235416650772095},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16606289148330688}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7057355046272278},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6301282644271851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5866632461547852},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4996061325073242},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.46233177185058594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45140019059181213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37941253185272217},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29752397537231445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29235416650772095},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16606289148330688},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:ris.utwente.nl:openaire/3646a431-5bf4-47e8-a285-1c042c41fbde","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/3646a431-5bf4-47e8-a285-1c042c41fbde","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bochev, M A & Golub, G H 2006, 'A Class of Nonsymmetric Preconditioners for Saddle Point Problems', SIAM journal on matrix analysis and applications, vol. 27, no. Technical/4, 10.1137/040618680, pp. 1125-1149. https://doi.org/10.1137/040618680","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:ris.utwente.nl:openaire/0fe0c83e-a802-4476-adf3-bbed7eb4962c","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/0fe0c83e-a802-4476-adf3-bbed7eb4962c","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bochev, M A & Golub, G H 2005, A class of nonsymmetric preconditioners for saddle point problems. Memoranda Mathematical Sciences, no. 1786, University of Twente, Enschede.","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:ut:oai:ris.utwente.nl:publications/0fe0c83e-a802-4476-adf3-bbed7eb4962c","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/a-class-of-nonsymmetric-preconditioners-for-saddle-point-problems(0fe0c83e-a802-4476-adf3-bbed7eb4962c).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:ut:oai:ris.utwente.nl:publications/4894f1b0-ee5a-4e80-8fe0-da66baa226b3","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/a-class-of-nonsymmetric-preconditioners-for-saddle-point-problems(4894f1b0-ee5a-4e80-8fe0-da66baa226b3).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:ut:oai:ris.utwente.nl:publications/75c3cdba-be0d-4c00-bc2a-7f313decf004","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/a-class-of-nonsymmetric-preconditioners-for-saddle-point-problems(75c3cdba-be0d-4c00-bc2a-7f313decf004).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"pmh:oai:ris.utwente.nl:openaire/3646a431-5bf4-47e8-a285-1c042c41fbde","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/3646a431-5bf4-47e8-a285-1c042c41fbde","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bochev, M A & Golub, G H 2006, 'A Class of Nonsymmetric Preconditioners for Saddle Point Problems', SIAM journal on matrix analysis and applications, vol. 27, no. Technical/4, 10.1137/040618680, pp. 1125-1149. https://doi.org/10.1137/040618680","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2900665543","https://openalex.org/W2780294397","https://openalex.org/W2161815683","https://openalex.org/W2901108086","https://openalex.org/W1985527365","https://openalex.org/W2109732432","https://openalex.org/W2522042480","https://openalex.org/W3020983548","https://openalex.org/W2219786281","https://openalex.org/W2884588126","https://openalex.org/W1970706285","https://openalex.org/W2597078233","https://openalex.org/W1971157997","https://openalex.org/W1986317308","https://openalex.org/W3187165158","https://openalex.org/W2495613491","https://openalex.org/W2927468811","https://openalex.org/W1981655180","https://openalex.org/W2172999760","https://openalex.org/W3196680557"],"abstract_inverted_index":{"For":[0],"iterative":[1,84],"solution":[2,63,89],"of":[3,19,29,49,59,64,72,77,90,96],"saddle":[4],"point":[5],"problems,":[6],"a":[7,27,65],"nonsymmetric":[8],"preconditioning":[9],"is":[10,37,53,105],"studied":[11],"which,":[12],"with":[13,39,88],"respect":[14,40],"to":[15,41],"the":[16,20,35,42,46,50,60,73,97,102],"upper-left":[17,51],"block":[18,52,104],"system":[21],"matrix,":[22],"can":[23,75],"be":[24,76],"seen":[25],"as":[26],"variant":[28],"SSOR.":[30],"An":[31],"idealized":[32],"situation":[33],"where":[34],"SSOR":[36],"taken":[38],"skew-symmetric":[43],"part":[44,48],"plus":[45],"diagonal":[47],"analyzed":[54],"in":[55,81],"detail.":[56],"Since":[57],"action":[58],"preconditioner":[61,74],"involves":[62],"Schur":[66],"complement":[67],"system,":[68],"an":[69,82],"inexact":[70],"form":[71],"interest.":[78],"This":[79],"results":[80],"inner-outer":[83],"process.":[85],"Numerical":[86],"experiments":[87],"linearized":[91],"Navier-Stokes":[92],"equations":[93],"demonstrate":[94],"efficiency":[95],"new":[98],"preconditioner,":[99],"especially":[100],"when":[101],"left-upper":[103],"far":[106],"from":[107],"symmetric.":[108]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
