{"id":"https://openalex.org/W3012821083","doi":"https://doi.org/10.1515/cmam-2020-0037","title":"Dimensionally Consistent Preconditioning for Saddle-Point Problems","display_name":"Dimensionally Consistent Preconditioning for Saddle-Point Problems","publication_year":2021,"publication_date":"2021-05-18","ids":{"openalex":"https://openalex.org/W3012821083","doi":"https://doi.org/10.1515/cmam-2020-0037","mag":"3012821083"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2020-0037","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2020-0037","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.09478","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070215713","display_name":"Roland Herzog","orcid":"https://orcid.org/0000-0003-2164-6575"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Roland Herzog","raw_affiliation_strings":["Interdisciplinary Center for Scientific Computing , Heidelberg University , 69120 Heidelberg , Germany","Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Center for Scientific Computing , Heidelberg University , 69120 Heidelberg , Germany","institution_ids":["https://openalex.org/I223822909"]},{"raw_affiliation_string":"Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070215713"],"corresponding_institution_ids":["https://openalex.org/I223822909"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01606187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"3","first_page":"593","last_page":"607"},"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/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/T11416","display_name":"Numerical methods for differential equations","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.9015352725982666},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7579481601715088},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7202145457267761},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5747994184494019},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5421079993247986},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5324769020080566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5022826194763184},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.44549819827079773},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4341660737991333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4067416191101074},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3603556156158447},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10626816749572754},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08736583590507507}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.9015352725982666},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7579481601715088},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7202145457267761},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5747994184494019},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5421079993247986},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5324769020080566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5022826194763184},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.44549819827079773},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4341660737991333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4067416191101074},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3603556156158447},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10626816749572754},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08736583590507507},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1515/cmam-2020-0037","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2020-0037","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.09478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09478","pdf_url":"https://arxiv.org/pdf/2003.09478","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3012821083","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.09478","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.09478","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.09478","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.09478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09478","pdf_url":"https://arxiv.org/pdf/2003.09478","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7200000286102295}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3012821083.pdf","grobid_xml":"https://content.openalex.org/works/W3012821083.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W42183144","https://openalex.org/W822664379","https://openalex.org/W1674659126","https://openalex.org/W1820125862","https://openalex.org/W1966886095","https://openalex.org/W1980053021","https://openalex.org/W2018850201","https://openalex.org/W2024621437","https://openalex.org/W2026993378","https://openalex.org/W2029367872","https://openalex.org/W2037818443","https://openalex.org/W2055116131","https://openalex.org/W2059880466","https://openalex.org/W2070671253","https://openalex.org/W2075237894","https://openalex.org/W2090927004","https://openalex.org/W2094400909","https://openalex.org/W2141870784","https://openalex.org/W2148033377","https://openalex.org/W2200851658","https://openalex.org/W2397812866","https://openalex.org/W2524874423","https://openalex.org/W2524931594","https://openalex.org/W2547610994","https://openalex.org/W2911987163","https://openalex.org/W2963824427","https://openalex.org/W4211094263","https://openalex.org/W4231405723","https://openalex.org/W4245654886","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W3161010767","https://openalex.org/W3128652131","https://openalex.org/W1972733133","https://openalex.org/W2797502925","https://openalex.org/W3126137513","https://openalex.org/W2228652985","https://openalex.org/W1991214825","https://openalex.org/W2324337765","https://openalex.org/W2999312468","https://openalex.org/W2985019967","https://openalex.org/W2311723394","https://openalex.org/W2616191639","https://openalex.org/W2115566547","https://openalex.org/W2219225786","https://openalex.org/W2594508505","https://openalex.org/W206885282","https://openalex.org/W3202286773","https://openalex.org/W1495073934","https://openalex.org/W2186245037","https://openalex.org/W1550302145"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"preconditioned":[2],"iterative":[3],"solution":[4],"of":[5,10,18,44,69,81,94],"large-scale":[6],"saddle-point":[7,77,144],"systems":[8,145],"is":[9,31,64],"great":[11],"importance":[12],"in":[13,108,119],"numerous":[14],"application":[15],"areas,":[16],"many":[17,120],"them":[19],"involving":[20],"partial":[21],"differential":[22],"equations.":[23],"Robustness":[24],"with":[25,114],"respect":[26,115],"to":[27,56,86,98,112,116,138],"certain":[28],"problem":[29,117],"parameters":[30,96,118],"often":[32],"a":[33,53,91,124,133],"concern,":[34],"and":[35,59,135],"it":[36],"can":[37],"be":[38],"addressed":[39],"by":[40],"identifying":[41],"proper":[42],"scalings":[43],"preconditioner":[45],"building":[46],"blocks.":[47],"In":[48],"this":[49,109],"paper,":[50],"we":[51,84,126],"consider":[52],"new":[54,134],"perspective":[55],"finding":[57],"effective":[58],"robust":[60,141],"preconditioners.":[61],"Our":[62],"approach":[63],"based":[65,130],"on":[66],"the":[67,70,75,95,99,105],"consideration":[68],"natural":[71,92],"physical":[72,150],"units":[73],"underlying":[74],"respective":[76],"problem.":[78,100],"This":[79],"point":[80],"view,":[82],"which":[83],"refer":[85],"as":[87,132],"dimensional":[88,128],"consistency,":[89],"suggests":[90],"combination":[93],"intrinsic":[97],"It":[101],"turns":[102],"out":[103],"that":[104],"scaling":[106],"obtained":[107],"way":[110,137],"leads":[111],"robustness":[113],"relevant":[121],"cases.":[122],"As":[123],"consequence,":[125],"advertise":[127],"consistency":[129],"preconditioning":[131],"systematic":[136],"designing":[139],"parameter":[140],"preconditoners":[142],"for":[143,149],"arising":[146],"from":[147],"models":[148],"phenomena.":[151]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}