{"id":"https://openalex.org/W3090925531","doi":"https://doi.org/10.1080/10556788.2020.1827254","title":"Simultaneous iterative solutions for the trust-region and minimum eigenvalue subproblem","display_name":"Simultaneous iterative solutions for the trust-region and minimum eigenvalue subproblem","publication_year":2020,"publication_date":"2020-10-01","ids":{"openalex":"https://openalex.org/W3090925531","doi":"https://doi.org/10.1080/10556788.2020.1827254","mag":"3090925531"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2020.1827254","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2020.1827254","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","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/A5003778121","display_name":"Ioannis Akrotirianakis","orcid":null},"institutions":[{"id":"https://openalex.org/I122754148","display_name":"SAS Institute (United States)","ror":"https://ror.org/01093z329","country_code":"US","type":"company","lineage":["https://openalex.org/I122754148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I. G. Akrotirianakis","raw_affiliation_strings":["SAS Institute, Cary, NC, USA"],"affiliations":[{"raw_affiliation_string":"SAS Institute, Cary, NC, USA","institution_ids":["https://openalex.org/I122754148"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065607444","display_name":"M. Gratton","orcid":null},"institutions":[{"id":"https://openalex.org/I122754148","display_name":"SAS Institute (United States)","ror":"https://ror.org/01093z329","country_code":"US","type":"company","lineage":["https://openalex.org/I122754148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Gratton","raw_affiliation_strings":["SAS Institute, Cary, NC, USA"],"affiliations":[{"raw_affiliation_string":"SAS Institute, Cary, NC, USA","institution_ids":["https://openalex.org/I122754148"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079196169","display_name":"Joshua Griffin","orcid":"https://orcid.org/0000-0002-6738-0154"},"institutions":[{"id":"https://openalex.org/I122754148","display_name":"SAS Institute (United States)","ror":"https://ror.org/01093z329","country_code":"US","type":"company","lineage":["https://openalex.org/I122754148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. D. Griffin","raw_affiliation_strings":["SAS Institute, Cary, NC, USA"],"affiliations":[{"raw_affiliation_string":"SAS Institute, Cary, NC, USA","institution_ids":["https://openalex.org/I122754148"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036869039","display_name":"S. Yektamaram","orcid":null},"institutions":[{"id":"https://openalex.org/I122754148","display_name":"SAS Institute (United States)","ror":"https://ror.org/01093z329","country_code":"US","type":"company","lineage":["https://openalex.org/I122754148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Yektamaram","raw_affiliation_strings":["SAS Institute, Cary, NC, USA"],"affiliations":[{"raw_affiliation_string":"SAS Institute, Cary, NC, USA","institution_ids":["https://openalex.org/I122754148"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051406984","display_name":"Wanlei Zhou","orcid":"https://orcid.org/0000-0002-1680-2521"},"institutions":[{"id":"https://openalex.org/I122754148","display_name":"SAS Institute (United States)","ror":"https://ror.org/01093z329","country_code":"US","type":"company","lineage":["https://openalex.org/I122754148"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. Zhou","raw_affiliation_strings":["SAS Institute, Cary, NC, USA"],"affiliations":[{"raw_affiliation_string":"SAS Institute, Cary, NC, USA","institution_ids":["https://openalex.org/I122754148"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5051406984"],"corresponding_institution_ids":["https://openalex.org/I122754148"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15795083,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"2","first_page":"692","last_page":"711"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9918000102043152,"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/trust-region","display_name":"Trust region","score":0.8626848459243774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7655810117721558},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.639583945274353},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5648369789123535},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5469435453414917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46268975734710693},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14773857593536377}],"concepts":[{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.8626848459243774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7655810117721558},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.639583945274353},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5648369789123535},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5469435453414917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46268975734710693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14773857593536377},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"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/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2020.1827254","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2020.1827254","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W1563737017","https://openalex.org/W1748199557","https://openalex.org/W1964217357","https://openalex.org/W1974888421","https://openalex.org/W1978618727","https://openalex.org/W1980431326","https://openalex.org/W2000389939","https://openalex.org/W2014168697","https://openalex.org/W2025975230","https://openalex.org/W2027257397","https://openalex.org/W2035080386","https://openalex.org/W2057141432","https://openalex.org/W2058885431","https://openalex.org/W2063690908","https://openalex.org/W2068685638","https://openalex.org/W2075184363","https://openalex.org/W2085137170","https://openalex.org/W2128836543","https://openalex.org/W2710596724","https://openalex.org/W2804136872","https://openalex.org/W2810319121","https://openalex.org/W3027959458","https://openalex.org/W3103067505","https://openalex.org/W3122661961","https://openalex.org/W4240022917","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2185500884","https://openalex.org/W3090925531","https://openalex.org/W2056399580","https://openalex.org/W2516748375","https://openalex.org/W2025931822","https://openalex.org/W947388129","https://openalex.org/W1983977627","https://openalex.org/W1973378639","https://openalex.org/W2081369546","https://openalex.org/W2188943855"],"abstract_inverted_index":{"Given":[0],"the":[1,30,44,54,92,112,126,145,162],"inability":[2],"to":[3,11,68,79,179],"foresee":[4],"all":[5,51],"possible":[6],"scenarios,":[7],"it":[8],"is":[9],"justified":[10],"desire":[12],"an":[13],"efficient":[14],"trust-region":[15,36,63],"subproblem":[16,37,97,172],"solver":[17,98,110,173],"capable":[18],"of":[19,24,56,116,164],"delivering":[20],"any":[21],"desired":[22],"level":[23],"accuracy":[25,31],"on":[26,43],"demand;":[27],"that":[28,99],"is,":[29],"obtainable":[32],"for":[33],"a":[34,104],"given":[35],"should":[38],"not":[39,122,142],"be":[40,80,131,159],"partially":[41],"dependent":[42],"problem":[45],"itself.":[46],"Current":[47],"state-of-the-art":[48],"iterative":[49,62,94,181],"eigensolvers":[50],"fall":[52],"into":[53],"class":[55],"restarted":[57,136],"Lanczos":[58,70,137,147],"methods;":[59,71],"whereas,":[60],"current":[61,146],"solvers":[64,166],"at":[65,100],"best":[66],"reduce":[67],"unrestarted":[69],"which":[72,120],"in":[73,161],"this":[74,88],"context":[75,163],"are":[76],"well":[77],"known":[78],"numerically":[81],"unstable":[82],"with":[83],"impractical":[84],"memory":[85],"requirements.":[86],"In":[87],"paper,":[89],"we":[90],"present":[91],"first":[93],"trust":[95],"region":[96],"its":[101,139],"core":[102],"contains":[103],"robust":[105],"and":[106,118,129],"practical":[107],"eigensolver.":[108],"Our":[109],"leverages":[111],"recently":[113],"announced":[114],"work":[115],"Stathopoulos":[117],"Orginos":[119],"has":[121],"been":[123],"noticed":[124],"by":[125,150],"optimization":[127],"community":[128],"can":[130,158],"utilized":[132,160],"because,":[133],"unlike":[134],"other":[135],"methods,":[138],"restarts":[140],"do":[141],"necessarily":[143],"modify":[144],"sequence":[148],"generated":[149],"Conjugate":[151],"Gradient":[152],"methods":[153],"(CG).":[154],"This":[155],"innovated":[156],"strategy":[157],"TR":[165,171,182],"as":[167],"well.":[168],"Moreover,":[169],"our":[170],"adds":[174],"negligible":[175],"computational":[176],"overhead":[177],"compared":[178],"existing":[180],"approaches.":[183]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}