{"id":"https://openalex.org/W2064561706","doi":"https://doi.org/10.1137/070707713","title":"Fast Condition Estimation for a Class of Structured Eigenvalue Problems","display_name":"Fast Condition Estimation for a Class of Structured Eigenvalue Problems","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2064561706","doi":"https://doi.org/10.1137/070707713","mag":"2064561706"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/070707713","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5078470824","display_name":"Alan J. Laub","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. J. Laub","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047496441","display_name":"Jianlin Xia","orcid":"https://orcid.org/0000-0002-9653-9312"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Xia","raw_affiliation_strings":["xiaj@math.purdue.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"xiaj@math.purdue.edu#TAB#","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.602,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":9,"citation_normalized_percentile":{"value":0.740936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":83,"max":84},"biblio":{"volume":"30","issue":"4","first_page":"1658","last_page":"1676"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997,"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":0.9997,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9954,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/flops","display_name":"FLOPS","score":0.5795059},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.54536873},{"id":"https://openalex.org/keywords/matrix-free-methods","display_name":"Matrix-free methods","score":0.4655085},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.41212136}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7792067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.76245},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7331581},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.6411255},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.61979854},{"id":"https://openalex.org/C3826847","wikidata":"https://www.wikidata.org/wiki/Q188768","display_name":"FLOPS","level":2,"score":0.5795059},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.54536873},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48222315},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4682962},{"id":"https://openalex.org/C54219892","wikidata":"https://www.wikidata.org/wiki/Q4080929","display_name":"Matrix-free methods","level":4,"score":0.4655085},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.41212136},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37353545},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36837155},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.28326166},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.24899828},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24293736},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.115076244},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/070707713","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":23,"referenced_works":["https://openalex.org/W1488044055","https://openalex.org/W1832266099","https://openalex.org/W1994809819","https://openalex.org/W2003501910","https://openalex.org/W2006603714","https://openalex.org/W2007447263","https://openalex.org/W2007649028","https://openalex.org/W2013737143","https://openalex.org/W2017641901","https://openalex.org/W2024918578","https://openalex.org/W2029435698","https://openalex.org/W2037620736","https://openalex.org/W2038011353","https://openalex.org/W2060881944","https://openalex.org/W2065402083","https://openalex.org/W2066447076","https://openalex.org/W2069415575","https://openalex.org/W2070984764","https://openalex.org/W2088748973","https://openalex.org/W2105591391","https://openalex.org/W2114583457","https://openalex.org/W2149733240","https://openalex.org/W296618920"],"related_works":["https://openalex.org/W4300096078","https://openalex.org/W4288408952","https://openalex.org/W3182794668","https://openalex.org/W2953378572","https://openalex.org/W2924352133","https://openalex.org/W2300674980","https://openalex.org/W2064561706","https://openalex.org/W1994155896","https://openalex.org/W1964591699","https://openalex.org/W1605345756"],"abstract_inverted_index":{"We":[0,59],"present":[1],"a":[2,11,64],"fast":[3],"condition":[4,71,105],"estimation":[5,72,78],"algorithm":[6,79,102],"for":[7,31,74,83,107,121],"the":[8,69,96,99,134,139],"eigenvalues":[9,109],"of":[10,13,52,68,87,98,138],"class":[12],"structured":[14,29,115],"matrices.":[15,27],"These":[16],"matrices":[17,33,53],"are":[18,34,54,118,130],"low":[19],"rank":[20],"modifications":[21],"to":[22,132],"Hermitian,":[23],"skew-Hermitian,":[24],"and":[25,110,125,136],"unitary":[26],"Fast":[28],"operations":[30,62,117],"these":[32,57,61],"presented,":[35],"including":[36],"Schur":[37],"decomposition,":[38],"eigenvalue":[39,75,111,123],"block":[40],"swapping,":[41],"matrix":[42,116],"equation":[43],"solving,":[44],"compact":[45],"structure":[46],"reconstruction,":[47],"etc.":[48],"Compact":[49],"semiseparable":[50],"representations":[51],"used":[55,131],"in":[56,63,90],"operations.":[58],"use":[60],"new,":[65],"improved":[66],"version":[67],"statistical":[70],"method":[73],"problems.":[76],"The":[77,101,113],"costs":[80],"$\\mathrm{O}(n^2)$":[81],"flops":[82],"all":[84],"eigenvalues,":[85],"instead":[86],"$\\mathrm{O}(n^3)$":[88],"as":[89],"traditional":[91],"algorithms,":[92],"where":[93],"n":[94],"is":[95],"order":[97],"matrix.":[100],"provides":[103],"reliable":[104],"estimates":[106],"both":[108],"clusters.":[112],"proposed":[114],"also":[119],"useful":[120],"additional":[122],"problems":[124],"other":[126],"applications.":[127],"Numerical":[128],"examples":[129],"illustrate":[133],"reliability":[135],"efficiency":[137],"algorithm.":[140]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2064561706","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-03-19T20:37:36.765419","created_date":"2016-06-24"}