{"id":"https://openalex.org/W1988099423","doi":"https://doi.org/10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m","title":"Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors","display_name":"Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1988099423","doi":"https://doi.org/10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m","mag":"1988099423"},"language":"en","primary_location":{"id":"doi:10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5029985184","display_name":"Alan Andrew","orcid":"https://orcid.org/0000-0002-4865-5562"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU","SG"],"is_corresponding":true,"raw_author_name":"Alan L. Andrew","raw_affiliation_strings":["Mathematics Department, La Trobe University, Bundoora, Victoria 3083, Australia","La Trobe University","National University of Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, La Trobe University, Bundoora, Victoria 3083, Australia","institution_ids":["https://openalex.org/I196829312"]},{"raw_affiliation_string":"La Trobe University","institution_ids":["https://openalex.org/I196829312"]},{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109412865","display_name":"Roger C. E. Tan","orcid":"https://orcid.org/0009-0009-3531-2294"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU","SG"],"is_corresponding":false,"raw_author_name":"Roger C. E. Tan","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, Singapore 119260","National University of Singapore","La Trobe University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, Singapore 119260","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"La Trobe University","institution_ids":["https://openalex.org/I196829312"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029985184"],"corresponding_institution_ids":["https://openalex.org/I165932596","https://openalex.org/I196829312"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.4615,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.64395973,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"4","first_page":"151","last_page":"167"},"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":0.9979000091552734,"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":0.9975000023841858,"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/mathematics","display_name":"Mathematics","score":0.8306372165679932},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8151810169219971},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6927631497383118},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5206441283226013},{"id":"https://openalex.org/keywords/modal-matrix","display_name":"Modal matrix","score":0.5019853115081787},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors-of-the-second-derivative","display_name":"Eigenvalues and eigenvectors of the second derivative","score":0.49968957901000977},{"id":"https://openalex.org/keywords/defective-matrix","display_name":"Defective matrix","score":0.4980628490447998},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.47026094794273376},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.4538102149963379},{"id":"https://openalex.org/keywords/eigenvalue-perturbation","display_name":"Eigenvalue perturbation","score":0.42734843492507935},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42113351821899414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3590342402458191},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3237871527671814},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3094894289970398},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.13359680771827698},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10545703768730164},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.0882677435874939}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8306372165679932},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8151810169219971},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6927631497383118},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5206441283226013},{"id":"https://openalex.org/C73772418","wikidata":"https://www.wikidata.org/wiki/Q6888018","display_name":"Modal matrix","level":5,"score":0.5019853115081787},{"id":"https://openalex.org/C65203669","wikidata":"https://www.wikidata.org/wiki/Q5348916","display_name":"Eigenvalues and eigenvectors of the second derivative","level":4,"score":0.49968957901000977},{"id":"https://openalex.org/C36967811","wikidata":"https://www.wikidata.org/wiki/Q5251123","display_name":"Defective matrix","level":5,"score":0.4980628490447998},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.47026094794273376},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.4538102149963379},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.42734843492507935},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42113351821899414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3590342402458191},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3237871527671814},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3094894289970398},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.13359680771827698},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10545703768730164},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.0882677435874939},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/103450","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103450","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/F4320320577","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27"},{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W61948969","https://openalex.org/W645542774","https://openalex.org/W1548154618","https://openalex.org/W1563885070","https://openalex.org/W1573717114","https://openalex.org/W1850049434","https://openalex.org/W1980177911","https://openalex.org/W1982605007","https://openalex.org/W1983977627","https://openalex.org/W1993865793","https://openalex.org/W2002567101","https://openalex.org/W2002739878","https://openalex.org/W2002986350","https://openalex.org/W2009767545","https://openalex.org/W2012246388","https://openalex.org/W2014955175","https://openalex.org/W2015321063","https://openalex.org/W2015632604","https://openalex.org/W2016008052","https://openalex.org/W2024414262","https://openalex.org/W2024477167","https://openalex.org/W2026735869","https://openalex.org/W2028875955","https://openalex.org/W2033721499","https://openalex.org/W2043561826","https://openalex.org/W2046025274","https://openalex.org/W2047200029","https://openalex.org/W2047947072","https://openalex.org/W2058172093","https://openalex.org/W2075117203","https://openalex.org/W2075117326","https://openalex.org/W2084876298","https://openalex.org/W2088306234","https://openalex.org/W2092540247","https://openalex.org/W2094631898","https://openalex.org/W2107560917","https://openalex.org/W2108950527","https://openalex.org/W2119500683","https://openalex.org/W2126955722","https://openalex.org/W2140715711","https://openalex.org/W2154559668","https://openalex.org/W2166377759","https://openalex.org/W2946289328","https://openalex.org/W4253016148","https://openalex.org/W4293079168","https://openalex.org/W6602577983"],"related_works":["https://openalex.org/W330769287","https://openalex.org/W2497112068","https://openalex.org/W2379354442","https://openalex.org/W3022668387","https://openalex.org/W184897903","https://openalex.org/W2478378501","https://openalex.org/W2171901332","https://openalex.org/W2057517924","https://openalex.org/W45285127","https://openalex.org/W1987168303"],"abstract_inverted_index":{"Recently":[0],"the":[1,9,12,19,32,47,55,62],"authors":[2],"proposed":[3],"a":[4],"simultaneous":[5,63],"iteration":[6],"algorithm":[7,36,58],"for":[8,71],"computation":[10],"of":[11,15,22,34,65],"partial":[13],"derivatives":[14],"repeated":[16,48,68],"eigenvalues":[17],"and":[18,37,54,67],"corresponding":[20],"eigenvectors":[21],"matrices":[23],"depending":[24],"on":[25],"several":[26,41],"real":[27],"variables.":[28],"This":[29],"paper":[30],"analyses":[31],"properties":[33],"that":[35,46],"extends":[38],"it":[39],"in":[40],"ways.":[42],"The":[43],"previous":[44],"requirement":[45],"eigenvalue":[49],"be":[50],"dominant":[51],"is":[52],"relaxed,":[53],"new":[56],"generalized":[57],"given":[59],"here":[60],"allows":[61],"treatment":[64],"simple":[66],"eigenvalues.":[69],"Methods":[70],"accelerating":[72],"convergence":[73],"are":[74],"examined.":[75],"Numerical":[76],"results":[77],"support":[78],"our":[79],"theoretical":[80],"analysis.":[81],"Copyright":[82],"\u00a9":[83],"2000":[84],"John":[85],"Wiley":[86],"&":[87],"Sons,":[88],"Ltd.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}
