{"id":"https://openalex.org/W2143150153","doi":"https://doi.org/10.1002/nla.1680020302","title":"Some inverse eigenproblems for Jacobi and arrow matrices","display_name":"Some inverse eigenproblems for Jacobi and arrow matrices","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W2143150153","doi":"https://doi.org/10.1002/nla.1680020302","mag":"2143150153"},"language":"en","primary_location":{"id":"doi:10.1002/nla.1680020302","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020302","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/A5045367328","display_name":"Carlos F. Borges","orcid":"https://orcid.org/0000-0002-8236-6131"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Carlos F. Borges","raw_affiliation_strings":["Code Ma/Bc, Naval Postgraduate School, Monterey, CA 93943, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Code Ma/Bc, Naval Postgraduate School, Monterey, CA 93943, USA","institution_ids":["https://openalex.org/I35364215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026463882","display_name":"R. Frezza","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ruggero Frezza","raw_affiliation_strings":["DEI, Universita di Padova, via Gradenigo 6/A, 35131 Padova, Italy","DEI, Universit\u00e0 di Padova - Via Gradenigo 6/A, 35131 Padova - Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEI, Universita di Padova, via Gradenigo 6/A, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"DEI, Universit\u00e0 di Padova - Via Gradenigo 6/A, 35131 Padova - Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060633436","display_name":"William B. Gragg","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William B. Gragg","raw_affiliation_strings":["Code Ma/Gr, Naval Postgraduate School, Monterey, CA 93943, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Code Ma/Gr, Naval Postgraduate School, Monterey, CA 93943, USA","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045367328"],"corresponding_institution_ids":["https://openalex.org/I35364215"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.23838326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2","issue":"3","first_page":"195","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9643999934196472,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9578999876976013,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8541887998580933},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.8068386316299438},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7356961965560913},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6301078200340271},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5689512491226196},{"id":"https://openalex.org/keywords/jacobi-method","display_name":"Jacobi method","score":0.5488539338111877},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5101726055145264},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.474725604057312},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46702030301094055},{"id":"https://openalex.org/keywords/jacobi-eigenvalue-algorithm","display_name":"Jacobi eigenvalue algorithm","score":0.45701104402542114},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33816292881965637},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3203807473182678},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.168320894241333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08230629563331604}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8541887998580933},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.8068386316299438},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7356961965560913},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6301078200340271},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5689512491226196},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.5488539338111877},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5101726055145264},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.474725604057312},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46702030301094055},{"id":"https://openalex.org/C135648419","wikidata":"https://www.wikidata.org/wiki/Q1677726","display_name":"Jacobi eigenvalue algorithm","level":3,"score":0.45701104402542114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33816292881965637},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3203807473182678},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.168320894241333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08230629563331604},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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":2,"locations":[{"id":"doi:10.1002/nla.1680020302","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020302","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:calhoun.nps.edu:10945/29610","is_oa":false,"landing_page_url":"http://hdl.handle.net/10945/29610","pdf_url":null,"source":{"id":"https://openalex.org/S4306400952","display_name":"Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35364215","host_organization_name":"Naval Postgraduate School","host_organization_lineage":["https://openalex.org/I35364215"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1034080277","https://openalex.org/W2005423095","https://openalex.org/W2013737143","https://openalex.org/W2017641901","https://openalex.org/W2035881097","https://openalex.org/W2041437078","https://openalex.org/W2054188927","https://openalex.org/W2058221770","https://openalex.org/W2059586807","https://openalex.org/W2065197309","https://openalex.org/W2074551980","https://openalex.org/W2132718937","https://openalex.org/W2141091191","https://openalex.org/W2251882576","https://openalex.org/W2568342123","https://openalex.org/W3022136271","https://openalex.org/W4235709941"],"related_works":["https://openalex.org/W967419144","https://openalex.org/W2381807195","https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W1607100495","https://openalex.org/W183135790","https://openalex.org/W2381799323","https://openalex.org/W1990844505","https://openalex.org/W2020828929","https://openalex.org/W2010853573"],"abstract_inverted_index":{"Abstract":[0],"We":[1,25],"consider":[2],"the":[3,61],"problem":[4],"of":[5],"reconstructing":[6],"Jacobi":[7],"matrices":[8,13],"and":[9],"real":[10],"symmetric":[11],"arrow":[12],"from":[14],"two":[15],"eigenpairs.":[16],"Algorithms":[17],"for":[18,60],"solving":[19],"these":[20],"inverse":[21],"problems":[22],"are":[23,29],"presented.":[24],"show":[26],"that":[27,43],"there":[28],"reasonable":[30],"conditions":[31],"under":[32],"which":[33],"this":[34],"reconstruction":[35,47],"is":[36,41,57],"always":[37],"possible.":[38],"Moreover,":[39],"it":[40],"seen":[42],"in":[44],"certain":[45],"cases":[46],"can":[48],"proceed":[49],"with":[50,65],"little":[51],"or":[52],"no":[53],"cancellation.":[54],"The":[55],"algorithm":[56],"particularly":[58],"elegant":[59],"tridiagonal":[62],"matrix":[63],"associated":[64],"a":[66],"bidiagonal":[67],"singular":[68],"value":[69],"decomposition.":[70]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
