{"id":"https://openalex.org/W1984543816","doi":"https://doi.org/10.1137/s0036144596305582","title":"From Potential Theory to Matrix Iterations in Six Steps","display_name":"From Potential Theory to Matrix Iterations in Six Steps","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1984543816","doi":"https://doi.org/10.1137/s0036144596305582","mag":"1984543816"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144596305582","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144596305582","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5062904806","display_name":"Tobin A. Driscoll","orcid":"https://orcid.org/0000-0002-1490-2545"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tobin A. Driscoll","raw_affiliation_strings":["University of Colorado \u2010 Boulder"],"affiliations":[{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064083862","display_name":"Kim-Chuan Toh","orcid":"https://orcid.org/0000-0001-7204-8933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim-Chuan Toh","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065363123","display_name":"Lloyd N. Trefethen","orcid":"https://orcid.org/0000-0003-2504-1709"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lloyd N. Trefethen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062904806"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":6.611,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.97172684,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"547","last_page":"578"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9912999868392944,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9900000095367432,"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/biconjugate-gradient-stabilized-method","display_name":"Biconjugate gradient stabilized method","score":0.8101176023483276},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7510154247283936},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.6777031421661377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6676294803619385},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6443536281585693},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6054762601852417},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5813567042350769},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5730898380279541},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5381383299827576},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5333777666091919},{"id":"https://openalex.org/keywords/biconjugate-gradient-method","display_name":"Biconjugate gradient method","score":0.4211944341659546},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3486230671405792},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3236815333366394},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2967434525489807},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.2714087963104248},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24091166257858276},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.21278133988380432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2092442810535431},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1378958523273468}],"concepts":[{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.8101176023483276},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7510154247283936},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6777031421661377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6676294803619385},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6443536281585693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6054762601852417},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5813567042350769},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5730898380279541},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5381383299827576},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5333777666091919},{"id":"https://openalex.org/C89408827","wikidata":"https://www.wikidata.org/wiki/Q855169","display_name":"Biconjugate gradient method","level":5,"score":0.4211944341659546},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3486230671405792},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3236815333366394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2967434525489807},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.2714087963104248},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24091166257858276},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.21278133988380432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2092442810535431},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1378958523273468},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0036144596305582","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144596305582","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/103305","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103305","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","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":"Scopus","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.33.545","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.545","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/iterations.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.365.1341","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.365.1341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.udel.edu/~driscoll/papers/1998-DriscollTohTrefethen-547.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.37.9019","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.9019","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://amath-www.colorado.edu/appm/faculty/tad/research/sixsteps.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":89,"referenced_works":["https://openalex.org/W8840247","https://openalex.org/W18468166","https://openalex.org/W1488341329","https://openalex.org/W1506342804","https://openalex.org/W1509839166","https://openalex.org/W1539593706","https://openalex.org/W1539600348","https://openalex.org/W1546004968","https://openalex.org/W1560263223","https://openalex.org/W1563653928","https://openalex.org/W1571187512","https://openalex.org/W1575701986","https://openalex.org/W1576347883","https://openalex.org/W1590577697","https://openalex.org/W1590879322","https://openalex.org/W1854226152","https://openalex.org/W1958022197","https://openalex.org/W1964771000","https://openalex.org/W1970832443","https://openalex.org/W1977061454","https://openalex.org/W1977208243","https://openalex.org/W1980357388","https://openalex.org/W1981745143","https://openalex.org/W1982602023","https://openalex.org/W1985014527","https://openalex.org/W1985536181","https://openalex.org/W1994084361","https://openalex.org/W1997225065","https://openalex.org/W1998836311","https://openalex.org/W2002639157","https://openalex.org/W2018850201","https://openalex.org/W2019027232","https://openalex.org/W2019327644","https://openalex.org/W2020282540","https://openalex.org/W2020804487","https://openalex.org/W2021810545","https://openalex.org/W2021846130","https://openalex.org/W2023413246","https://openalex.org/W2028476543","https://openalex.org/W2030995892","https://openalex.org/W2040298674","https://openalex.org/W2041214608","https://openalex.org/W2045370380","https://openalex.org/W2047151498","https://openalex.org/W2048981224","https://openalex.org/W2049627148","https://openalex.org/W2049644675","https://openalex.org/W2052149646","https://openalex.org/W2053949358","https://openalex.org/W2057337348","https://openalex.org/W2060375549","https://openalex.org/W2061813658","https://openalex.org/W2064101518","https://openalex.org/W2069195908","https://openalex.org/W2069766942","https://openalex.org/W2075351838","https://openalex.org/W2075962499","https://openalex.org/W2080301514","https://openalex.org/W2082463306","https://openalex.org/W2082492903","https://openalex.org/W2082923923","https://openalex.org/W2085259167","https://openalex.org/W2090687449","https://openalex.org/W2100384730","https://openalex.org/W2102247210","https://openalex.org/W2116284739","https://openalex.org/W2117366131","https://openalex.org/W2117919754","https://openalex.org/W2117949169","https://openalex.org/W2130860589","https://openalex.org/W2136866714","https://openalex.org/W2137029533","https://openalex.org/W2140153041","https://openalex.org/W2143476164","https://openalex.org/W2155216327","https://openalex.org/W2314564916","https://openalex.org/W2316564661","https://openalex.org/W2321956437","https://openalex.org/W2330913512","https://openalex.org/W2479560584","https://openalex.org/W2726774827","https://openalex.org/W2798909945","https://openalex.org/W3003821699","https://openalex.org/W3022909171","https://openalex.org/W3141390961","https://openalex.org/W3155122104","https://openalex.org/W4206097460","https://openalex.org/W4229978573","https://openalex.org/W4254574205"],"related_works":["https://openalex.org/W2069713958","https://openalex.org/W2371875888","https://openalex.org/W1620763245","https://openalex.org/W2486238093","https://openalex.org/W1510662217","https://openalex.org/W2130308425","https://openalex.org/W2592349247","https://openalex.org/W2073922269","https://openalex.org/W1848849174","https://openalex.org/W2129625121"],"abstract_inverted_index":{"The":[0],"theory":[1,49],"of":[2,5,12,29,47,79,84],"the":[3,59],"convergence":[4,35],"Krylov":[6],"subspace":[7],"iterations":[8],"for":[9],"linear":[10],"systems":[11],"equations":[13],"(conjugate":[14],"gradients,":[15,17],"biconjugate":[16],"GMRES,":[18],"QMR,":[19],"Bi-CGSTAB,":[20],"and":[21,74,88],"so":[22],"on)":[23],"is":[24],"reviewed.":[25],"For":[26],"a":[27,45,77],"computation":[28,61],"this":[30,63],"kind,":[31],"an":[32],"estimated":[33],"asymptotic":[34],"factor":[36],"$\\rho":[37],"\\le":[38],"1$":[39],"can":[40],"be":[41],"derived":[42],"by":[43,76],"solving":[44],"problem":[46],"potential":[48],"or":[50],"conformal":[51,86],"mapping.":[52],"Six":[53],"approximations":[54,68],"are":[55,69],"involved":[56],"in":[57,71],"relating":[58],"actual":[60],"to":[62],"scalar":[64],"estimate.":[65],"These":[66],"six":[67],"discussed":[70],"asystematic":[72],"way":[73],"illustrated":[75],"sequence":[78],"examples":[80],"computed":[81],"with":[82],"tools":[83],"numerical":[85],"mapping":[87],"semidefinite":[89],"programming.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}