{"id":"https://openalex.org/W2464658298","doi":"https://doi.org/10.1137/15m1016266","title":"Sensitivity and Computation of a Defective Eigenvalue","display_name":"Sensitivity and Computation of a Defective Eigenvalue","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2464658298","doi":"https://doi.org/10.1137/15m1016266","mag":"2464658298"},"language":"en","primary_location":{"id":"doi:10.1137/15m1016266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1016266","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.03185","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zhonggang Zeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhonggang Zeng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0856,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.80228081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"37","issue":"2","first_page":"798","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.7462999820709229,"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":0.7462999820709229,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.0430000014603138,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.027899999171495438,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8305000066757202},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7329000234603882},{"id":"https://openalex.org/keywords/jordan-matrix","display_name":"Jordan matrix","score":0.6401000022888184},{"id":"https://openalex.org/keywords/eigenvalue-perturbation","display_name":"Eigenvalue perturbation","score":0.6069999933242798},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5958999991416931},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5674999952316284},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48069998621940613},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4788999855518341},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.4731000065803528}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8773000240325928},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8305000066757202},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7329000234603882},{"id":"https://openalex.org/C89890916","wikidata":"https://www.wikidata.org/wiki/Q3738073","display_name":"Jordan matrix","level":3,"score":0.6401000022888184},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.6069999933242798},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5958999991416931},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5674999952316284},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4788999855518341},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.4684999883174896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46779999136924744},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.46380001306533813},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.46299999952316284},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4507000148296356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4327000081539154},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.40549999475479126},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.3257000148296356},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2930999994277954},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.2572000026702881},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C109565186","wikidata":"https://www.wikidata.org/wiki/Q6766437","display_name":"Eigenvalue algorithm","level":5,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1016266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1016266","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:arXiv.org:2103.03185","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.03185","pdf_url":"https://arxiv.org/pdf/2103.03185","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.03185","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.03185","pdf_url":"https://arxiv.org/pdf/2103.03185","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1969125683","https://openalex.org/W1992967356","https://openalex.org/W2002986350","https://openalex.org/W2013853256","https://openalex.org/W2015321063","https://openalex.org/W2025639042","https://openalex.org/W2035953755","https://openalex.org/W2042803184","https://openalex.org/W2056636900","https://openalex.org/W2065304525","https://openalex.org/W2072500636","https://openalex.org/W2119459069","https://openalex.org/W2617854063","https://openalex.org/W4205138698"],"related_works":[],"abstract_inverted_index":{"A":[0],"defective":[1,41,67],"eigenvalue":[2,42,68],"is":[3,27,69,93],"well":[4],"documented":[5],"to":[6,9,45],"be":[7,81],"hypersensitive":[8],"data":[10],"perturbations":[11,46],"and":[12,52],"round-off":[13],"errors,":[14],"making":[15],"it":[16,79],"a":[17,35,40,66,72],"formidable":[18],"challenge":[19],"in":[20],"numerical":[21,63],"computation":[22,64],"particularly":[23],"when":[24],"the":[25,49,53,91],"matrix":[26,92],"known":[28],"through":[29],"approximate":[30],"data.":[31],"This":[32],"paper":[33],"establishes":[34],"finitely":[36],"bounded":[37],"sensitivity":[38],"of":[39,65],"with":[43],"respect":[44],"that":[47,78],"preserve":[48],"geometric":[50],"multiplicity":[51],"smallest":[54],"Jordan":[55],"block":[56],"size.":[57],"Based":[58],"on":[59],"this":[60],"perturbation":[61],"theory,":[62],"regularized":[70],"as":[71],"well-posed":[73],"least":[74],"squares":[75],"problem":[76],"so":[77],"can":[80],"accurately":[82],"carried":[83],"out":[84],"using":[85],"floating":[86],"point":[87],"arithmetic":[88],"even":[89],"if":[90],"perturbed.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-07-22T00:00:00"}