{"id":"https://openalex.org/W2044333641","doi":"https://doi.org/10.1137/070688742","title":"Jacobi Correction Equation, Line Search, and Conjugate Gradients in Hermitian Eigenvalue Computation I: Computing an Extreme Eigenvalue","display_name":"Jacobi Correction Equation, Line Search, and Conjugate Gradients in Hermitian Eigenvalue Computation I: Computing an Extreme Eigenvalue","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2044333641","doi":"https://doi.org/10.1137/070688742","mag":"2044333641"},"language":"en","primary_location":{"id":"doi:10.1137/070688742","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070688742","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5014344269","display_name":"Evgueni Ovtchinnikov","orcid":"https://orcid.org/0000-0002-9359-6514"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"E. E. Ovtchinnikov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014344269"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6464,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.83999865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"46","issue":"5","first_page":"2567","last_page":"2592"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9988999962806702,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.8082588315010071},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8067235946655273},{"id":"https://openalex.org/keywords/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.7436478734016418},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6498557329177856},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6398046016693115},{"id":"https://openalex.org/keywords/rayleigh-quotient-iteration","display_name":"Rayleigh quotient iteration","score":0.6333683729171753},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6001524329185486},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.5723462700843811},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.5517407059669495},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5445390939712524},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.47415226697921753},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"Inverse iteration","score":0.4373885989189148},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4311334192752838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41775065660476685},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.4152787923812866},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3546164035797119},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.30530399084091187},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.27118897438049316},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.2664197087287903},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1260814368724823},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1068321168422699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08631187677383423}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8082588315010071},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8067235946655273},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.7436478734016418},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6498557329177856},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6398046016693115},{"id":"https://openalex.org/C117586675","wikidata":"https://www.wikidata.org/wiki/Q7298489","display_name":"Rayleigh quotient iteration","level":4,"score":0.6333683729171753},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6001524329185486},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.5723462700843811},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.5517407059669495},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5445390939712524},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.47415226697921753},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.4373885989189148},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4311334192752838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41775065660476685},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.4152787923812866},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3546164035797119},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.30530399084091187},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27118897438049316},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.2664197087287903},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1260814368724823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1068321168422699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08631187677383423},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070688742","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070688742","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1323373","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1323373/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM J. Numer. Anal. , 46    pp. 2567-2592.   (2008)      ","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1502316316","https://openalex.org/W1509860612","https://openalex.org/W1970733490","https://openalex.org/W1979522268","https://openalex.org/W1997862149","https://openalex.org/W2006729027","https://openalex.org/W2009964554","https://openalex.org/W2012231377","https://openalex.org/W2014851363","https://openalex.org/W2015295339","https://openalex.org/W2027436456","https://openalex.org/W2032371871","https://openalex.org/W2037034729","https://openalex.org/W2039127720","https://openalex.org/W2045512849","https://openalex.org/W2051142108","https://openalex.org/W2059241250","https://openalex.org/W2059586807","https://openalex.org/W2066463080","https://openalex.org/W2068226994","https://openalex.org/W2070645684","https://openalex.org/W2076995010","https://openalex.org/W2079508024","https://openalex.org/W2086160340","https://openalex.org/W2092320654","https://openalex.org/W2096539214","https://openalex.org/W2101700471","https://openalex.org/W2106965455","https://openalex.org/W2109443444","https://openalex.org/W2124386592","https://openalex.org/W2142184851","https://openalex.org/W2156553331","https://openalex.org/W2316564661","https://openalex.org/W2350991510","https://openalex.org/W3102398037","https://openalex.org/W4235703716"],"related_works":["https://openalex.org/W1976066180","https://openalex.org/W2035592577","https://openalex.org/W2049348317","https://openalex.org/W2574203527","https://openalex.org/W2172969761","https://openalex.org/W1989286647","https://openalex.org/W3188219351","https://openalex.org/W4205803876","https://openalex.org/W4297437581","https://openalex.org/W4388185085"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,55,90,129,140],"concerned":[3],"with":[4],"the":[5,17,28,31,40,44,47,52,60,63,72,75,79,87,95,98,103,110,125,143,146,162,165],"convergence":[6,100,134],"properties":[7,101,160],"of":[8,11,19,23,30,46,59,86,97,109,119,161,164],"iterative":[9],"algorithms":[10,36,111,123],"conjugate":[12,121,137],"gradient":[13,61,122,138],"type":[14],"applied":[15,93],"to":[16,94],"computation":[18],"an":[20,107],"extreme":[21],"eigenvalue":[22,76,147],"a":[24,56,84,132],"Hermitian":[25],"operator":[26,163],"via":[27],"optimization":[29],"Rayleigh":[32,48],"quotient":[33,49],"functional.":[34],"The":[35,114,154],"in":[37,51,74,112,145],"focus":[38],"employ":[39],"line":[41,80],"search":[42,65,81,88],"for":[43,71,136],"extremum":[45],"functional":[50],"direction":[53,89],"that":[54],"linear":[57],"combination":[58],"and":[62,92,124,131],"previous":[64],"direction.":[66],"An":[67],"asymptotically":[68],"explicit":[69],"equation":[70],"reduction":[73,105,144],"error":[77,104,148],"after":[78,106,149],"step":[82],"as":[83],"function":[85],"derived":[91],"analysis":[96,156],"local":[99,115],"(i.e.,":[102],"iteration)":[108],"question.":[113],"(stepwise)":[116],"asymptotic":[117],"equivalence":[118],"various":[120],"generalized":[126],"Davidson":[127],"method":[128],"proved,":[130],"new":[133],"estimate":[135],"iterations":[139],"derived,":[141],"showing":[142],"any":[150],"two":[151],"consecutive":[152],"iterations.":[153],"paper's":[155],"extensively":[157],"employs":[158],"remarkable":[159],"so-called":[166],"Jacobi":[167],"orthogonal":[168],"complement":[169],"correction":[170],"equation.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}
