{"id":"https://openalex.org/W2040786813","doi":"https://doi.org/10.1080/00207160701396387","title":"Frobenius norm minimization and probing for preconditioning","display_name":"Frobenius norm minimization and probing for preconditioning","publication_year":2007,"publication_date":"2007-08-01","ids":{"openalex":"https://openalex.org/W2040786813","doi":"https://doi.org/10.1080/00207160701396387","mag":"2040786813"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701396387","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701396387","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://mediatum.ub.tum.de/node?id=1417803","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067705772","display_name":"Thomas Huckle","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"T. Huckle","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen , Boltzmannstr. 3, D-85748, Garching, Germany","Fakult\u00e4t F\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen , Boltzmannstr. 3, D-85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Fakult\u00e4t F\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064249998","display_name":"A. Kallischko","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"A. Kallischko","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen , Boltzmannstr. 3, D-85748, Garching, Germany","Fakult\u00e4t F\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen , Boltzmannstr. 3, D-85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Fakult\u00e4t F\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067705772"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":1.123,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.78133654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"84","issue":"8","first_page":"1225","last_page":"1248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9972000122070312,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9036836624145508},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7557146549224854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6950124502182007},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6505871415138245},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6132200360298157},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5100794434547424},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4843326807022095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4634867012500763},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.45772868394851685},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.42882007360458374},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.42564278841018677},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41040778160095215},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3514723777770996},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3288455009460449},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.303921639919281},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18905878067016602},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15487077832221985},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10059168934822083},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07435902953147888}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9036836624145508},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7557146549224854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6950124502182007},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6505871415138245},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6132200360298157},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5100794434547424},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4843326807022095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4634867012500763},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.45772868394851685},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.42882007360458374},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.42564278841018677},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41040778160095215},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3514723777770996},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3288455009460449},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.303921639919281},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18905878067016602},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15487077832221985},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10059168934822083},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07435902953147888},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160701396387","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701396387","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1417803","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1417803","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"article"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1417803","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1417803","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W174510205","https://openalex.org/W194487525","https://openalex.org/W1511121222","https://openalex.org/W1538878357","https://openalex.org/W1973590515","https://openalex.org/W1987573671","https://openalex.org/W1994805693","https://openalex.org/W2000374859","https://openalex.org/W2005040897","https://openalex.org/W2007579628","https://openalex.org/W2014223575","https://openalex.org/W2026502086","https://openalex.org/W2029087005","https://openalex.org/W2032354159","https://openalex.org/W2038516134","https://openalex.org/W2046224229","https://openalex.org/W2110290705","https://openalex.org/W2133248904","https://openalex.org/W2217655847","https://openalex.org/W2733756498","https://openalex.org/W7026563768"],"related_works":["https://openalex.org/W3046775784","https://openalex.org/W2382988560","https://openalex.org/W2024149451","https://openalex.org/W3031624508","https://openalex.org/W2977980606","https://openalex.org/W2525981419","https://openalex.org/W2956259592","https://openalex.org/W2033698563","https://openalex.org/W4322732133","https://openalex.org/W2604862712"],"abstract_inverted_index":{"In":[0],"this":[1,66,81],"paper":[2],"we":[3,47,72,95],"introduce":[4,96],"a":[5,16,49,59],"new":[6,97,119],"method":[7],"for":[8,11,51,91,99],"defining":[9],"preconditioners":[10,27,37,53,120],"the":[12,23,30,34,40,85],"iterative":[13],"solution":[14],"of":[15,18,25,36],"system":[17,94],"linear":[19,93],"equations.":[20],"By":[21],"generalizing":[22],"class":[24,35],"modified":[26],"(e.g.":[28,44],"MILU),":[29],"interface":[31],"probing,":[32],"and":[33,113,126],"related":[38],"to":[39,58,80,123],"Frobenius":[41],"norm":[42],"minimization":[43],"FSAI,":[45],"SPAI)":[46,69],"develop":[48],"toolbox":[50],"computing":[52],"that":[54,117],"are":[55,87],"improved":[56],"relative":[57],"given":[60,76],"small":[61],"probing":[62,70,82],"subspace.":[63,83],"Furthermore,":[64],"by":[65],"MSPAI":[67],"(modified":[68],"approach":[71],"can":[73],"improve":[74],"any":[75],"preconditioner":[77],"with":[78],"respect":[79],"All":[84],"computations":[86],"embarrassingly":[88],"parallel.":[89],"Additionally,":[90],"symmetric":[92],"techniques":[98],"symmetrizing":[100],"preconditioners.":[101],"Many":[102],"numerical":[103],"examples,":[104],"e.g.":[105],"from":[106],"PDE":[107],"applications":[108],"such":[109],"as":[110],"domain":[111],"decomposition":[112],"Stokes":[114],"problem,":[115],"show":[116],"these":[118],"often":[121],"lead":[122],"faster":[124],"convergence":[125],"smaller":[127],"condition":[128],"numbers.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}