{"id":"https://openalex.org/W2072684432","doi":"https://doi.org/10.1137/130905216","title":"On the Inverse Symmetric Quadratic Eigenvalue Problem","display_name":"On the Inverse Symmetric Quadratic Eigenvalue Problem","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2072684432","doi":"https://doi.org/10.1137/130905216","mag":"2072684432"},"language":"en","primary_location":{"id":"doi:10.1137/130905216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130905216","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/A5012007500","display_name":"Peter Lancaster","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Peter Lancaster","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059067253","display_name":"I. Zaballa","orcid":"https://orcid.org/0000-0002-6113-9079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ion Zaballa","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012007500"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.66950584,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.8590951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"35","issue":"1","first_page":"254","last_page":"278"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.993399977684021,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8364269733428955},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8085275292396545},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6899744868278503},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5492267608642578},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5217674374580383},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5080499649047852},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46476706862449646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4626380503177643},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45965996384620667},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45324718952178955},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43481749296188354},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.4234035611152649},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3301229476928711},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12602922320365906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8364269733428955},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8085275292396545},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6899744868278503},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5492267608642578},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5217674374580383},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5080499649047852},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46476706862449646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4626380503177643},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45965996384620667},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45324718952178955},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43481749296188354},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.4234035611152649},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3301229476928711},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12602922320365906},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130905216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130905216","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W42127144","https://openalex.org/W626183909","https://openalex.org/W1964594672","https://openalex.org/W1967890524","https://openalex.org/W1970606629","https://openalex.org/W1973069366","https://openalex.org/W1985502054","https://openalex.org/W2006165168","https://openalex.org/W2007032864","https://openalex.org/W2015845899","https://openalex.org/W2017967170","https://openalex.org/W2039078552","https://openalex.org/W2043561826","https://openalex.org/W2076426180","https://openalex.org/W2086049388","https://openalex.org/W2128978199","https://openalex.org/W2153333084","https://openalex.org/W2167868875","https://openalex.org/W2316727981","https://openalex.org/W2317205703"],"related_works":["https://openalex.org/W2189494880","https://openalex.org/W269925151","https://openalex.org/W3096788047","https://openalex.org/W2379041201","https://openalex.org/W2101513891","https://openalex.org/W4386731488","https://openalex.org/W2024156986","https://openalex.org/W2995216836","https://openalex.org/W2027798872","https://openalex.org/W4385817362"],"abstract_inverted_index":{"The":[0],"detailed":[1,27],"spectral":[2,42],"structure":[3],"of":[4,20,29,32,83],"symmetric,":[5],"algebraic,":[6],"quadratic":[7,85],"eigenvalue":[8],"problems":[9,31],"has":[10],"been":[11],"developed":[12],"recently.":[13],"In":[14],"this":[15,68],"paper":[16],"we":[17],"take":[18],"advantage":[19],"these":[21,61],"canonical":[22],"forms":[23],"to":[24,74,90],"provide":[25],"a":[26,64],"analysis":[28],"inverse":[30],"the":[33,37,41,45,53,75,78,84],"following":[34],"form:":[35],"construct":[36],"coefficient":[38],"matrices":[39],"from":[40],"data":[43,48],"including":[44],"classical":[46],"eigenvalue/eigenvector":[47],"and":[49,80],"sign":[50],"characteristics":[51],"for":[52],"real":[54],"eigenvalues.":[55],"An":[56],"orthogonality":[57],"condition":[58],"dependent":[59],"on":[60],"signs":[62],"plays":[63],"vital":[65],"role":[66],"in":[67],"construction.":[69],"Special":[70],"attention":[71],"is":[72],"paid":[73],"cases":[76],"when":[77],"leading":[79],"trailing":[81],"coefficients":[82],"matrix":[86],"polynomial":[87],"are":[88],"prescribed":[89],"be":[91],"positive":[92],"definite.":[93]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
