{"id":"https://openalex.org/W578918596","doi":"https://doi.org/10.1137/140967994","title":"A Riemannian Newton Algorithm for Nonlinear Eigenvalue Problems","display_name":"A Riemannian Newton Algorithm for Nonlinear Eigenvalue Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W578918596","doi":"https://doi.org/10.1137/140967994","mag":"578918596"},"language":"en","primary_location":{"id":"doi:10.1137/140967994","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140967994","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and 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/A5102022536","display_name":"Zhi Zhao","orcid":"https://orcid.org/0000-0002-9338-5530"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhi Zhao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055283405","display_name":"Zheng\u2010Jian Bai","orcid":null},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng-Jian Bai","raw_affiliation_strings":["Xiamen University"],"affiliations":[{"raw_affiliation_string":"Xiamen University","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005037066","display_name":"Xiaoqing Jin","orcid":"https://orcid.org/0000-0002-8836-3505"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Xiao-Qing Jin","raw_affiliation_strings":["[University of Macau]"],"affiliations":[{"raw_affiliation_string":"[University of Macau]","institution_ids":["https://openalex.org/I204512498"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102022536"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.5507,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.96822283,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"36","issue":"2","first_page":"752","last_page":"774"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8685354590415955},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8544120788574219},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6354179382324219},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5710287690162659},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5698243379592896},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.5457578897476196},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5127692818641663},{"id":"https://openalex.org/keywords/positive-definiteness","display_name":"Positive definiteness","score":0.49407294392585754},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4871899485588074},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4510877728462219},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44709062576293945},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4405437707901001},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.43816226720809937},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4114103615283966},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4103579521179199},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.3827320337295532},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3395427167415619},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.11311587691307068},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09449762105941772}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8685354590415955},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8544120788574219},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6354179382324219},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5710287690162659},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5698243379592896},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.5457578897476196},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5127692818641663},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.49407294392585754},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4871899485588074},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4510877728462219},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44709062576293945},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4405437707901001},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.43816226720809937},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4114103615283966},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4103579521179199},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.3827320337295532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3395427167415619},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.11311587691307068},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09449762105941772},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140967994","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140967994","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.702.3828","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.702.3828","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.xmu.edu.cn/school/teacher/bai/papers/ZBJ15_SIMAX.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W648869842","https://openalex.org/W1544171083","https://openalex.org/W1585439088","https://openalex.org/W1804110266","https://openalex.org/W1966406013","https://openalex.org/W1971536112","https://openalex.org/W1974333117","https://openalex.org/W1981078764","https://openalex.org/W1996728110","https://openalex.org/W1997671037","https://openalex.org/W1998134546","https://openalex.org/W2007395042","https://openalex.org/W2020428152","https://openalex.org/W2028324955","https://openalex.org/W2045512849","https://openalex.org/W2046434053","https://openalex.org/W2048633871","https://openalex.org/W2051906496","https://openalex.org/W2052171888","https://openalex.org/W2057342157","https://openalex.org/W2078223384","https://openalex.org/W2079354271","https://openalex.org/W2086953401","https://openalex.org/W2090689930","https://openalex.org/W2092344142","https://openalex.org/W2098432400","https://openalex.org/W2098760944","https://openalex.org/W2110662303","https://openalex.org/W2132492255","https://openalex.org/W2149784569","https://openalex.org/W2156529323","https://openalex.org/W2162349032","https://openalex.org/W2166742209","https://openalex.org/W2169650761","https://openalex.org/W3029645440","https://openalex.org/W4248555053"],"related_works":["https://openalex.org/W3200169917","https://openalex.org/W2031270640","https://openalex.org/W2012255426","https://openalex.org/W2063906068","https://openalex.org/W2047871498","https://openalex.org/W2010012920","https://openalex.org/W2089895988","https://openalex.org/W2083194257","https://openalex.org/W2087978208","https://openalex.org/W2996136316"],"abstract_inverted_index":{"We":[0],"give":[1],"the":[2,25,34,40,44,49,53,69,72],"formulation":[3],"of":[4,13,39,48,52,71],"a":[5,11,19,58],"Riemannian":[6,50],"Newton":[7],"algorithm":[8],"for":[9,75],"solving":[10,76],"class":[12],"nonlinear":[14],"eigenvalue":[15],"problems":[16],"by":[17],"minimizing":[18],"total":[20,54],"energy":[21,55],"function":[22,56],"subject":[23],"to":[24,67],"orthogonality":[26],"constraint.":[27],"Under":[28],"some":[29],"mild":[30],"assumptions,":[31],"we":[32],"establish":[33],"global":[35],"and":[36],"quadratic":[37],"convergence":[38],"proposed":[41,73],"method.":[42],"Moreover,":[43],"positive":[45],"definiteness":[46],"condition":[47],"Hessian":[51],"at":[57],"solution":[59],"is":[60],"derived.":[61],"Some":[62],"numerical":[63],"tests":[64],"are":[65],"reported":[66],"illustrate":[68],"efficiency":[70],"method":[74],"large-scale":[77],"problems.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}