{"id":"https://openalex.org/W1977444623","doi":"https://doi.org/10.1137/s1064827599356900","title":"Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method","display_name":"Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1977444623","doi":"https://doi.org/10.1137/s1064827599356900","mag":"1977444623"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827599356900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599356900","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/A5060523944","display_name":"Jane Cullum","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jane K. Cullum","raw_affiliation_strings":["LOS Alamos National Laboratory"],"affiliations":[{"raw_affiliation_string":"LOS Alamos National Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]},{"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":10.3059,"has_fulltext":false,"cited_by_count":184,"citation_normalized_percentile":{"value":0.98655835,"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":"1318","last_page":"1332"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987999796867371,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9972000122070312,"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/preconditioner","display_name":"Preconditioner","score":0.925626277923584},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8865063786506653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8015080094337463},{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.737204372882843},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5737665891647339},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5400640964508057},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.52835613489151},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5196613073348999},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.49028828740119934},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4839623272418976},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.479729562997818},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.4779106080532074},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4566343128681183},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.44964608550071716},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4233304560184479},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.41119813919067383},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3663402199745178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33114975690841675},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3150113821029663},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.26757317781448364},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.19771268963813782},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.15575996041297913},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14227795600891113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11752912402153015}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.925626277923584},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8865063786506653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8015080094337463},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.737204372882843},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5737665891647339},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5400640964508057},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.52835613489151},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5196613073348999},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.49028828740119934},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4839623272418976},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.479729562997818},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.4779106080532074},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4566343128681183},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.44964608550071716},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4233304560184479},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.41119813919067383},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3663402199745178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33114975690841675},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3150113821029663},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.26757317781448364},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.19771268963813782},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.15575996041297913},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14227795600891113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11752912402153015},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s1064827599356900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599356900","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:10.1.1.125.4422","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.4422","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/bct.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.41.6617","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.6617","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/robust.ps.gz","raw_type":"text"},{"id":"pmh:oai:ricerca.sns.it:11384/75282","is_oa":false,"landing_page_url":"http://hdl.handle.net/11384/75282","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":34,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1511480514","https://openalex.org/W1546004968","https://openalex.org/W1971440257","https://openalex.org/W1973607402","https://openalex.org/W1977631509","https://openalex.org/W1985968347","https://openalex.org/W1986310461","https://openalex.org/W1986652366","https://openalex.org/W1992208469","https://openalex.org/W1994805693","https://openalex.org/W1998388190","https://openalex.org/W1999086185","https://openalex.org/W2010666500","https://openalex.org/W2013336356","https://openalex.org/W2014216434","https://openalex.org/W2019814079","https://openalex.org/W2026502086","https://openalex.org/W2038516134","https://openalex.org/W2046407882","https://openalex.org/W2052079843","https://openalex.org/W2058273413","https://openalex.org/W2064003621","https://openalex.org/W2078311192","https://openalex.org/W2082434918","https://openalex.org/W2086648616","https://openalex.org/W2089099677","https://openalex.org/W2110290705","https://openalex.org/W2125543813","https://openalex.org/W2155017090","https://openalex.org/W2156588317","https://openalex.org/W2156736893","https://openalex.org/W4230121183","https://openalex.org/W4245301022"],"related_works":["https://openalex.org/W2098528027","https://openalex.org/W2005717169","https://openalex.org/W3159557833","https://openalex.org/W3159907817","https://openalex.org/W2798336637","https://openalex.org/W2183734858","https://openalex.org/W2353110519","https://openalex.org/W640673894","https://openalex.org/W4225835417","https://openalex.org/W7156132"],"abstract_inverted_index":{"We":[0,46],"present":[1],"a":[2,38,53],"variant":[3],"of":[4,62,66,71,83],"the":[5,32,60],"AINV":[6],"factorized":[7],"sparse":[8],"approximate":[9,55],"inverse":[10,56],"algorithm":[11],"which":[12],"is":[13,24],"applicable":[14],"to":[15,52],"any":[16],"symmetric":[17],"positive":[18],"definite":[19],"matrix.":[20],"The":[21,69],"new":[22],"preconditioner":[23],"breakdown-free":[25],"and,":[26],"when":[27],"used":[28],"in":[29,37],"conjunction":[30],"with":[31],"conjugate":[33],"gradient":[34],"method,":[35],"results":[36,70],"reliable":[39],"solver":[40],"for":[41],"highly":[42],"ill-conditioned":[43],"linear":[44,76],"systems.":[45],"also":[47],"investigate":[48],"an":[49],"alternative":[50],"approach":[51],"stable":[54],"algorithm,":[57],"based":[58],"on":[59,74],"idea":[61],"diagonally":[63],"compensated":[64],"reduction":[65],"matrix":[67],"entries.":[68],"numerical":[72],"tests":[73],"challenging":[75],"systems":[77],"arising":[78],"from":[79],"finite":[80],"element":[81],"modeling":[82],"elasticity":[84],"and":[85],"diffusion":[86],"problems":[87],"are":[88],"presented.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
