{"id":"https://openalex.org/W2083070741","doi":"https://doi.org/10.1137/s0895479895288851","title":"The Minimum Eigenvalue of a Symmetric Positive-Definite Toeplitz Matrix and Rational Hermitian Interpolation","display_name":"The Minimum Eigenvalue of a Symmetric Positive-Definite Toeplitz Matrix and Rational Hermitian Interpolation","publication_year":1997,"publication_date":"1997-07-01","ids":{"openalex":"https://openalex.org/W2083070741","doi":"https://doi.org/10.1137/s0895479895288851","mag":"2083070741"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479895288851","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895288851","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/A5015044906","display_name":"Wolfgang Mackens","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wolfgang Mackens","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110652573","display_name":"Heinrich Vo\u00df","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heinrich Voss","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7012,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.96471015,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"18","issue":"3","first_page":"521","last_page":"534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9958999752998352,"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"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9811999797821045,"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":0.8680504560470581},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8369487524032593},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8195009231567383},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7740548849105835},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7049591541290283},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5769875645637512},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5476835370063782},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5258848071098328},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5006260871887207},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.4520518481731415},{"id":"https://openalex.org/keywords/bisection-method","display_name":"Bisection method","score":0.4468977749347687},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4350847005844116},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3268139958381653},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32369422912597656},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28457173705101013}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8680504560470581},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8369487524032593},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8195009231567383},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7740548849105835},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7049591541290283},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5769875645637512},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5476835370063782},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5258848071098328},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5006260871887207},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.4520518481731415},{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.4468977749347687},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4350847005844116},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3268139958381653},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32369422912597656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28457173705101013},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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},{"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0895479895288851","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895288851","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:hdl:10068/184343","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/184343","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"I - Miscellaneous"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.57.5820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.5820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.tu-harburg.de/mat/SCHRIFTEN/toep1.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1977519779","https://openalex.org/W1980763573","https://openalex.org/W1988889311","https://openalex.org/W2019833178","https://openalex.org/W2025986317","https://openalex.org/W2058221770","https://openalex.org/W2070760846","https://openalex.org/W2088548459","https://openalex.org/W2092085096","https://openalex.org/W2101042764"],"related_works":["https://openalex.org/W2361901126","https://openalex.org/W2070080181","https://openalex.org/W2015339619","https://openalex.org/W1826911152","https://openalex.org/W4237208466","https://openalex.org/W1981713296","https://openalex.org/W2021675158","https://openalex.org/W2081925639","https://openalex.org/W4386707620","https://openalex.org/W1963784504"],"abstract_inverted_index":{"A":[0],"novel":[1],"method":[2,40,84,94],"for":[3],"computing":[4],"the":[5,18,39,49,60,72,79,83],"minimal":[6],"eigenvalue":[7,74],"of":[8,20,29,38,48,57,63,82,85],"a":[9,27,32,96],"symmetric":[10],"positive-definite":[11],"Toeplitz":[12],"matrix":[13],"is":[14,26,75],"presented.":[15],"Similar":[16],"to":[17,70,90],"algorithm":[19],"Cybenko":[21,86],"and":[22,31,87],"Van":[23,88],"Loan,":[24],"it":[25],"combination":[28],"bisection":[30],"root":[33],"finding":[34],"method.":[35],"Both":[36],"phases":[37],"are":[41],"accelerated":[42],"considerably":[43],"by":[44],"rational":[45],"Hermitian":[46],"interpolation":[47],"secular":[50],"equation.":[51],"For":[52],"randomly":[53],"generated":[54],"test":[55],"problems":[56],"dimension":[58],"800":[59],"average":[61],"number":[62],"linear":[64],"systems":[65],"which":[66,77],"must":[67],"be":[68],"solved":[69],"determine":[71],"smallest":[73],"6.6,":[76],"reduces":[78],"computational":[80],"cost":[81],"Loan":[89],"approximately":[91],"35%.":[92],"The":[93],"includes":[95],"rigorous":[97],"error":[98],"bound.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}