{"id":"https://openalex.org/W1963652031","doi":"https://doi.org/10.1002/nla.600","title":"Left conjugate gradient method for non\u2010Hermitian linear systems","display_name":"Left conjugate gradient method for non\u2010Hermitian linear systems","publication_year":2008,"publication_date":"2008-07-09","ids":{"openalex":"https://openalex.org/W1963652031","doi":"https://doi.org/10.1002/nla.600","mag":"1963652031"},"language":"en","primary_location":{"id":"doi:10.1002/nla.600","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.600","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","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/A5038365025","display_name":"Liping Wang","orcid":"https://orcid.org/0000-0002-7765-2387"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li\u2010Ping Wang","raw_affiliation_strings":["Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China","Department of Mathematics College of Science Nanjing University of Aeronautics and Astronautics Nanjing 210016, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Department of Mathematics College of Science Nanjing University of Aeronautics and Astronautics Nanjing 210016, People's Republic of China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110798385","display_name":"Yu-Hong Dai","orcid":"https://orcid.org/0000-0003-4147-1346"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu\u2010Hong Dai","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People's Republic of China","Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People's Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110798385"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.4081,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64772922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"10","first_page":"891","last_page":"909"},"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":0.9972000122070312,"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.9016056656837463},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7987470626831055},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.7557194232940674},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7030633091926575},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.7017715573310852},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6892896890640259},{"id":"https://openalex.org/keywords/complex-conjugate","display_name":"Complex conjugate","score":0.639938235282898},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.5273992419242859},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4789450764656067},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.459419310092926},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.4280853569507599},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3674194812774658},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33351656794548035},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2310670018196106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18482685089111328},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18318858742713928},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.11161303520202637},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05180978775024414}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.9016056656837463},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7987470626831055},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.7557194232940674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7030633091926575},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.7017715573310852},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6892896890640259},{"id":"https://openalex.org/C45542137","wikidata":"https://www.wikidata.org/wiki/Q381040","display_name":"Complex conjugate","level":2,"score":0.639938235282898},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.5273992419242859},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4789450764656067},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.459419310092926},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.4280853569507599},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3674194812774658},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33351656794548035},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2310670018196106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18482685089111328},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18318858742713928},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.11161303520202637},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05180978775024414},{"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":1,"locations":[{"id":"doi:10.1002/nla.600","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.600","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1571187512","https://openalex.org/W1971166562","https://openalex.org/W2020315201","https://openalex.org/W2028324784","https://openalex.org/W2039700854","https://openalex.org/W2055251260","https://openalex.org/W2066434958","https://openalex.org/W2069595221","https://openalex.org/W2085259167","https://openalex.org/W2087848595","https://openalex.org/W2108488673","https://openalex.org/W2140153041","https://openalex.org/W2155216327"],"related_works":["https://openalex.org/W2098528027","https://openalex.org/W3159557833","https://openalex.org/W2005717169","https://openalex.org/W3159907817","https://openalex.org/W2183734858","https://openalex.org/W2353110519","https://openalex.org/W3123621400","https://openalex.org/W2941778027","https://openalex.org/W640673894","https://openalex.org/W2388344948"],"abstract_inverted_index":{"Abstract":[0],"Recently,":[1],"Yuan":[2],"et":[3],"al":[4],".":[5],"(":[6],"BIT":[7],":":[8],"Numer.":[9],"Math.":[10],"2004;":[11],"44":[12],"(1):189\u2013207)":[13],"proposed":[14,94],"the":[15,41,47,53,60,73,77,83,90,93],"left":[16,55],"conjugate":[17,56],"gradient":[18],"(LCG)":[19],"method":[20,32,58,75],"for":[21,33],"real":[22,84],"positive\u2010definite":[23],"linear":[24,37],"systems.":[25,38],"This":[26],"paper":[27],"aims":[28],"to":[29,82],"generalize":[30],"their":[31],"solving":[34],"complex":[35],"non\u2010Hermitian":[36],"To":[39],"avoid":[40],"breakdown":[42,70],"that":[43,68],"possibly":[44],"occurred":[45],"in":[46,72],"LCG":[48,62,95],"method,":[49],"we":[50],"also":[51,80],"propose":[52],"block":[54,61,78],"direction":[57],"and":[59,76],"(BLCG)":[63],"method.":[64,96],"It":[65],"is":[66],"found":[67],"no":[69],"occurs":[71],"BLCG":[74],"idea":[79],"applies":[81],"nonsymmetric":[85],"case.":[86],"Numerical":[87],"experiments":[88],"demonstrate":[89],"usefulness":[91],"of":[92],"Copyright":[97],"\u00a9":[98],"2008":[99],"John":[100],"Wiley":[101],"&amp;":[102],"Sons,":[103],"Ltd.":[104]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
