{"id":"https://openalex.org/W2030922334","doi":"https://doi.org/10.1137/120879841","title":"Computing Derivatives of Repeated Eigenvalues and Corresponding Eigenvectors of Quadratic Eigenvalue Problems","display_name":"Computing Derivatives of Repeated Eigenvalues and Corresponding Eigenvectors of Quadratic Eigenvalue Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2030922334","doi":"https://doi.org/10.1137/120879841","mag":"2030922334"},"language":"en","primary_location":{"id":"doi:10.1137/120879841","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120879841","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/A5102419171","display_name":"Qian Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang Qian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029985184","display_name":"Alan Andrew","orcid":"https://orcid.org/0000-0002-4865-5562"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan L. Andrew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102966756","display_name":"Delin Chu","orcid":"https://orcid.org/0000-0001-7736-7490"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Delin Chu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109412865","display_name":"Roger C. E. Tan","orcid":"https://orcid.org/0009-0009-3531-2294"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roger C. E. Tan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9197,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.93648889,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"34","issue":"3","first_page":"1089","last_page":"1111"},"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":0.9955000281333923,"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":0.9782000184059143,"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":0.8744208216667175},{"id":"https://openalex.org/keywords/eigenvalue-perturbation","display_name":"Eigenvalue perturbation","score":0.8180791139602661},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors-of-the-second-derivative","display_name":"Eigenvalues and eigenvectors of the second derivative","score":0.7626994848251343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7502787113189697},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.6475951671600342},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5157699584960938},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5120673775672913},{"id":"https://openalex.org/keywords/defective-matrix","display_name":"Defective matrix","score":0.4831256568431854},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.4619596004486084},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4517858922481537},{"id":"https://openalex.org/keywords/spectrum-of-a-matrix","display_name":"Spectrum of a matrix","score":0.45016273856163025},{"id":"https://openalex.org/keywords/modal-matrix","display_name":"Modal matrix","score":0.426379919052124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3834618330001831},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.20828160643577576},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.1368069350719452},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.09420064091682434},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09017348289489746},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05500999093055725}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8744208216667175},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.8180791139602661},{"id":"https://openalex.org/C65203669","wikidata":"https://www.wikidata.org/wiki/Q5348916","display_name":"Eigenvalues and eigenvectors of the second derivative","level":4,"score":0.7626994848251343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7502787113189697},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.6475951671600342},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5157699584960938},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5120673775672913},{"id":"https://openalex.org/C36967811","wikidata":"https://www.wikidata.org/wiki/Q5251123","display_name":"Defective matrix","level":5,"score":0.4831256568431854},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.4619596004486084},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4517858922481537},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.45016273856163025},{"id":"https://openalex.org/C73772418","wikidata":"https://www.wikidata.org/wiki/Q6888018","display_name":"Modal matrix","level":5,"score":0.426379919052124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3834618330001831},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.20828160643577576},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.1368069350719452},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.09420064091682434},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09017348289489746},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05500999093055725},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120879841","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120879841","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:scholarbank.nus.edu.sg:10635/103029","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103029","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1548154618","https://openalex.org/W1605807425","https://openalex.org/W1968384821","https://openalex.org/W1970171319","https://openalex.org/W1970606629","https://openalex.org/W1976742810","https://openalex.org/W1982605007","https://openalex.org/W1983633411","https://openalex.org/W1988099423","https://openalex.org/W1993624135","https://openalex.org/W2012246388","https://openalex.org/W2015714858","https://openalex.org/W2024414262","https://openalex.org/W2038215198","https://openalex.org/W2042423781","https://openalex.org/W2046025274","https://openalex.org/W2051754724","https://openalex.org/W2053529276","https://openalex.org/W2063837515","https://openalex.org/W2085211606","https://openalex.org/W2089752880","https://openalex.org/W2090072003","https://openalex.org/W2092251581","https://openalex.org/W2100525669","https://openalex.org/W2126955722","https://openalex.org/W2134147834","https://openalex.org/W2138395440","https://openalex.org/W2140715711","https://openalex.org/W2163336887"],"related_works":["https://openalex.org/W330769287","https://openalex.org/W3022668387","https://openalex.org/W1987168303","https://openalex.org/W2379354442","https://openalex.org/W2497112068","https://openalex.org/W2478378501","https://openalex.org/W209453833","https://openalex.org/W4251966336","https://openalex.org/W818276166","https://openalex.org/W2077030276"],"abstract_inverted_index":{"We":[0,75],"consider":[1,63],"quadratic":[2],"eigenvalue":[3,73],"problems":[4],"in":[5,25,27],"which":[6,28],"the":[7,12,54,72,102],"coefficient":[8],"matrices,":[9],"and":[10,14,49,78,85,91],"hence":[11],"eigenvalues":[13,34,48,55,67,90],"eigenvectors,":[15,50],"are":[16,94],"functions":[17,30],"of":[18,47,89,104],"a":[19],"real":[20],"parameter.":[21],"Our":[22],"interest":[23],"is":[24],"cases":[26],"these":[29],"remain":[31],"differentiable":[32],"when":[33],"coincide.":[35],"Many":[36],"papers":[37],"have":[38],"been":[39],"devoted":[40],"to":[41,56],"numerical":[42],"methods":[43,106],"for":[44,82,107],"computing":[45,83],"derivatives":[46,88],"but":[51],"most":[52],"require":[53],"be":[57],"well":[58],"separated.":[59],"The":[60],"few":[61],"that":[62,93],"close":[64],"or":[65],"repeated":[66],"place":[68],"severe":[69],"restrictions":[70],"on":[71],"derivatives.":[74],"propose,":[76],"analyze,":[77],"test":[79],"new":[80],"algorithms":[81],"first":[84],"higher":[86],"order":[87],"eigenvectors":[92],"valid":[95],"much":[96],"more":[97],"generally.":[98],"Numerical":[99],"results":[100],"confirm":[101],"effectiveness":[103],"our":[105],"tightly":[108],"clustered":[109],"eigenvalues.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}