{"id":"https://openalex.org/W2976783422","doi":"https://doi.org/10.1080/00207160.2019.1673378","title":"On global convergence of subspace projection methods for Hermitian eigenvalue problems","display_name":"On global convergence of subspace projection methods for Hermitian eigenvalue problems","publication_year":2019,"publication_date":"2019-09-27","ids":{"openalex":"https://openalex.org/W2976783422","doi":"https://doi.org/10.1080/00207160.2019.1673378","mag":"2976783422"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2019.1673378","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1673378","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5057510698","display_name":"Cun-Qiang Miao","orcid":"https://orcid.org/0000-0002-9171-0889"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cun-Qiang Miao","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066889105","display_name":"Xue-Yuan Tan","orcid":null},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xue-Yuan Tan","raw_affiliation_strings":["Jiangsu Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Jiangsu Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing, People's Republic of China","institution_ids":["https://openalex.org/I152031979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066889105"],"corresponding_institution_ids":["https://openalex.org/I152031979"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15362118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"97","issue":"10","first_page":"1982","last_page":"1993"},"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":0.9991000294685364,"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":0.9958999752998352,"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/lanczos-resampling","display_name":"Lanczos resampling","score":0.7673283815383911},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7658916711807251},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7097324132919312},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7018285989761353},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6801279783248901},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5934380888938904},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5454436540603638},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.511933445930481},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4985034465789795},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.48209574818611145},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.4785200357437134},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.45838209986686707},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4174373149871826},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4074413776397705},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28046607971191406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22830599546432495},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1294664442539215},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07176682353019714}],"concepts":[{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.7673283815383911},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7658916711807251},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7097324132919312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7018285989761353},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6801279783248901},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5934380888938904},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5454436540603638},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.511933445930481},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4985034465789795},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.48209574818611145},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.4785200357437134},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.45838209986686707},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4174373149871826},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4074413776397705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28046607971191406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22830599546432495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1294664442539215},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07176682353019714},{"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/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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2019.1673378","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1673378","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1314681659","display_name":null,"funder_award_id":"ZR2018BG002","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3125725589","display_name":null,"funder_award_id":"17KJB110008","funder_id":"https://openalex.org/F4320335440","funder_display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China"},{"id":"https://openalex.org/G3155566920","display_name":null,"funder_award_id":"11871280","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320335440","display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1963495087","https://openalex.org/W1984720662","https://openalex.org/W1993987675","https://openalex.org/W2009596258","https://openalex.org/W2019715448","https://openalex.org/W2023014562","https://openalex.org/W2027389940","https://openalex.org/W2033307991","https://openalex.org/W2050192005","https://openalex.org/W2052604766","https://openalex.org/W2055373329","https://openalex.org/W2059586807","https://openalex.org/W2060488365","https://openalex.org/W2086160340","https://openalex.org/W2087959096","https://openalex.org/W2116732229","https://openalex.org/W2142184851","https://openalex.org/W2480854438","https://openalex.org/W2513714633","https://openalex.org/W2576255697","https://openalex.org/W2605177467","https://openalex.org/W2806644665","https://openalex.org/W2900632289"],"related_works":["https://openalex.org/W3166616159","https://openalex.org/W4287126381","https://openalex.org/W1599640686","https://openalex.org/W1964004266","https://openalex.org/W1977732568","https://openalex.org/W4242776319","https://openalex.org/W3201061354","https://openalex.org/W2048659456","https://openalex.org/W1964074933","https://openalex.org/W4301683480"],"abstract_inverted_index":{"We":[0,51],"provide":[1],"a":[2,33,76],"concise":[3],"overview":[4],"of":[5,32,60,65],"some":[6,54],"iterative":[7],"approaches,":[8],"by":[9],"which":[10],"large":[11],"and":[12,47],"sparse":[13],"eigenvalue":[14],"problems":[15],"are":[16],"successfully":[17],"dealt":[18],"with.":[19],"Our":[20],"main":[21],"goal":[22],"in":[23,75,80],"this":[24],"paper":[25],"is":[26],"to":[27,56,84],"prove":[28],"the":[29,41,43,48,61,66,85],"global":[30,58,70],"convergence":[31,59,71],"few":[34],"state-of-the":[35],"art":[36],"iteration":[37],"methods,":[38],"such":[39],"as":[40],"Jacobi\u2013Davidson,":[42],"rational":[44],"Krylov":[45],"sequence":[46],"Lanczos":[49],"methods.":[50,68,87],"also":[52],"derive":[53],"conditions":[55],"ensure":[57],"corresponding":[62],"inexact":[63],"variants":[64],"above-mentioned":[67],"These":[69],"analyses":[72],"result":[73],"either":[74],"depth":[77],"understanding":[78],"or":[79],"an":[81],"efficient":[82],"improvement":[83],"original":[86]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}