{"id":"https://openalex.org/W1965394225","doi":"https://doi.org/10.1137/s1064827599361308","title":"Preconditioning Highly Indefinite and Nonsymmetric Matrices","display_name":"Preconditioning Highly Indefinite and Nonsymmetric Matrices","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1965394225","doi":"https://doi.org/10.1137/s1064827599361308","mag":"1965394225"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827599361308","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599361308","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5053109099","display_name":"Michele Benzi","orcid":"https://orcid.org/0000-0001-6099-0294"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michele Benzi","raw_affiliation_strings":["Emory University"],"affiliations":[{"raw_affiliation_string":"Emory University","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072341781","display_name":"John Courtney Haws","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John C. Haws","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053422141","display_name":"Miroslav T\u016fma","orcid":"https://orcid.org/0000-0003-2808-6929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miroslav Tuma","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053109099"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":6.5583,"has_fulltext":false,"cited_by_count":130,"citation_normalized_percentile":{"value":0.97075332,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"22","issue":"4","first_page":"1333","last_page":"1353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9965000152587891,"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/mathematics","display_name":"Mathematics","score":0.7291072607040405},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.592559278011322},{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.5916098952293396},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5900188088417053},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5498179197311401},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5208969116210938},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5196555852890015},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5012216567993164},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.489850252866745},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48359817266464233},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.47289955615997314},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.34662294387817383},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3404198884963989},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.233333557844162},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17785128951072693},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0840863287448883},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.07958251237869263}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7291072607040405},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.592559278011322},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.5916098952293396},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5900188088417053},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5498179197311401},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5208969116210938},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5196555852890015},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5012216567993164},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.489850252866745},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48359817266464233},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.47289955615997314},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34662294387817383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3404198884963989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.233333557844162},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17785128951072693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0840863287448883},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.07958251237869263},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s1064827599361308","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599361308","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.128.2845","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.2845","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/~benzi/Web_papers/bht.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.41.9363","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.9363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.uivt.cas.cz/~tuma/ps/indefinite.ps.gz","raw_type":"text"},{"id":"pmh:oai:ricerca.sns.it:11384/75293","is_oa":false,"landing_page_url":"http://hdl.handle.net/11384/75293","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W2524830","https://openalex.org/W18468166","https://openalex.org/W1506342804","https://openalex.org/W1560263223","https://openalex.org/W1972859808","https://openalex.org/W1977444623","https://openalex.org/W1977631509","https://openalex.org/W1984958506","https://openalex.org/W1986652366","https://openalex.org/W1992208469","https://openalex.org/W1994805693","https://openalex.org/W1998388190","https://openalex.org/W1999086185","https://openalex.org/W2008655047","https://openalex.org/W2014216434","https://openalex.org/W2017431061","https://openalex.org/W2020767300","https://openalex.org/W2023202674","https://openalex.org/W2038516134","https://openalex.org/W2040298674","https://openalex.org/W2041785146","https://openalex.org/W2044557804","https://openalex.org/W2046407882","https://openalex.org/W2048255281","https://openalex.org/W2052602889","https://openalex.org/W2058997431","https://openalex.org/W2086648616","https://openalex.org/W2089099677","https://openalex.org/W2108520826","https://openalex.org/W2113679823","https://openalex.org/W2132612821","https://openalex.org/W2140153041","https://openalex.org/W2143135486","https://openalex.org/W2155216327","https://openalex.org/W2156588317","https://openalex.org/W2156736893","https://openalex.org/W2169528473","https://openalex.org/W2206383384","https://openalex.org/W2249508874","https://openalex.org/W2327315803","https://openalex.org/W2331814142"],"related_works":["https://openalex.org/W2769503957","https://openalex.org/W4244038180","https://openalex.org/W1695940191","https://openalex.org/W582364689","https://openalex.org/W2584669347","https://openalex.org/W150331239","https://openalex.org/W1546004968","https://openalex.org/W2186959526","https://openalex.org/W2938161061","https://openalex.org/W1771660623"],"abstract_inverted_index":{"Standard":[0],"preconditioners,":[1],"like":[2],"incomplete":[3],"factorizations,":[4],"perform":[5],"well":[6],"when":[7],"the":[8,34,37,104],"coefficient":[9],"matrix":[10],"is":[11],"diagonally":[12],"dominant,":[13],"but":[14],"often":[15],"fail":[16],"on":[17,33],"general":[18,42],"sparse":[19,43],"matrices.":[20,44],"We":[21,86],"experiment":[22],"with":[23],"nonsymmetric":[24,90],"permutations":[25,46],"and":[26,47,54,63,66,106],"scalings":[27,48],"aimed":[28],"at":[29],"placing":[30],"large":[31],"entries":[32],"diagonal":[35],"in":[36],"context":[38],"of":[39,108],"preconditioning":[40],"for":[41,95],"The":[45],"are":[49,112],"those":[50],"developed":[51],"by":[52,64,115],"Olschowka":[53],"Neumaier":[55],"[Linear":[56],"Algebra":[57],"Appl.,":[58,72],"240":[59],"(1996),":[60],"pp.":[61,75],"131--151]":[62],"Duff":[65],"Koster":[67],"[SIAM":[68],"J.":[69],"Matrix":[70],"Anal.":[71],"20":[73],"(1999),":[74],"889--901;":[76],"Tech.":[77],"report":[78],"Ral-Tr-99-030,":[79],"Rutherford":[80],"Appleton":[81],"Laboratory,":[82],"Chilton,":[83],"UK,":[84],"1999].":[85],"target":[87],"highly":[88],"indefinite,":[89],"problems":[91],"that":[92,103],"cause":[93],"difficulties":[94],"preconditioned":[96,109],"iterative":[97,110],"solvers.":[98],"Our":[99],"numerical":[100],"experiments":[101],"indicate":[102],"reliability":[105],"performance":[107],"solvers":[111],"greatly":[113],"enhanced":[114],"such":[116],"preprocessing.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}