{"id":"https://openalex.org/W2059880466","doi":"https://doi.org/10.1137/100814767","title":"Nonstandard Norms and Robust Estimates for Saddle Point Problems","display_name":"Nonstandard Norms and Robust Estimates for Saddle Point Problems","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W2059880466","doi":"https://doi.org/10.1137/100814767","mag":"2059880466"},"language":"en","primary_location":{"id":"doi:10.1137/100814767","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814767","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/A5029325851","display_name":"Walter Zulehner","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Walter Zulehner","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029325851"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.2116,"has_fulltext":false,"cited_by_count":128,"citation_normalized_percentile":{"value":0.99112102,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"32","issue":"2","first_page":"536","last_page":"560"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8130007386207581},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7308443784713745},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7068980932235718},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6001290678977966},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5697002410888672},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5348846912384033},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.497013121843338},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.46454310417175293},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4544541835784912},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.42364269495010376},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38447174429893494},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.29800617694854736},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2870904207229614},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17281368374824524},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13176393508911133},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09969595074653625}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8130007386207581},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7308443784713745},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7068980932235718},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6001290678977966},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5697002410888672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5348846912384033},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.497013121843338},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.46454310417175293},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4544541835784912},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.42364269495010376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38447174429893494},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.29800617694854736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2870904207229614},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17281368374824524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13176393508911133},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09969595074653625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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":2,"locations":[{"id":"doi:10.1137/100814767","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814767","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.227.1142","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.1142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.numa.uni-linz.ac.at/Publications/List/2010/2010-07-r1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1483804921","https://openalex.org/W1966886095","https://openalex.org/W1972927314","https://openalex.org/W1980053021","https://openalex.org/W1993029535","https://openalex.org/W1997305590","https://openalex.org/W1999331305","https://openalex.org/W2015148405","https://openalex.org/W2018850201","https://openalex.org/W2022977680","https://openalex.org/W2029367872","https://openalex.org/W2050206349","https://openalex.org/W2053837400","https://openalex.org/W2055962135","https://openalex.org/W2057547853","https://openalex.org/W2062832849","https://openalex.org/W2065867295","https://openalex.org/W2083622979","https://openalex.org/W2085581918","https://openalex.org/W2092753238","https://openalex.org/W2094708316","https://openalex.org/W2141870784","https://openalex.org/W2162221417","https://openalex.org/W2177784766","https://openalex.org/W2488897645","https://openalex.org/W2561689613","https://openalex.org/W3149667697","https://openalex.org/W4232109906"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W3031624508","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W2551573654","https://openalex.org/W73248859","https://openalex.org/W1991285463","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072"],"abstract_inverted_index":{"In":[0,29],"this":[1],"paper":[2],"we":[3,61],"discuss":[4],"how":[5],"to":[6,16,66,83,88,102],"find":[7],"norms":[8,37,57,80,93],"for":[9,40,50,55,71,75,96,106],"parameter-dependent":[10],"saddle":[11,46],"point":[12,47],"problems":[13,70,110],"which":[14,81],"lead":[15,82,101],"robust":[17,84,114],"(i.e.,":[18],"parameter-independent)":[19],"estimates":[20,85],"of":[21,26,35,44],"the":[22,27,76,91,107],"solution":[23],"in":[24,119],"terms":[25],"data.":[28],"a":[30,33,41],"first":[31],"step":[32],"characterization":[34],"such":[36],"is":[38],"given":[39],"general":[42],"class":[43],"symmetric":[45],"problems.":[48,98],"Then,":[49],"special":[51],"cases,":[52],"explicit":[53],"formulas":[54],"these":[56,64,97],"are":[58],"derived.":[59],"Finally,":[60],"will":[62,100],"apply":[63],"results":[65],"distributed":[67],"optimal":[68],"control":[69],"elliptic":[72],"equations":[73],"and":[74,113],"Stokes":[77],"equations.":[78],"The":[79],"turn":[86],"out":[87],"differ":[89],"from":[90],"standard":[92],"typically":[94],"used":[95,118],"This":[99],"block":[103],"diagonal":[104],"preconditioners":[105],"corresponding":[108],"discretized":[109],"with":[111],"mesh-independent":[112],"convergence":[115],"rates":[116],"if":[117],"preconditioned":[120],"Krylov":[121],"subspace":[122],"methods.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":16}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}