{"id":"https://openalex.org/W2090832914","doi":"https://doi.org/10.1137/120869432","title":"Subspace Methods for Computing the Pseudospectral Abscissa and the Stability Radius","display_name":"Subspace Methods for Computing the Pseudospectral Abscissa and the Stability Radius","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2090832914","doi":"https://doi.org/10.1137/120869432","mag":"2090832914"},"language":"en","primary_location":{"id":"doi:10.1137/120869432","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120869432","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":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/198547","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084601962","display_name":"Daniel Kre\u00dfner","orcid":"https://orcid.org/0000-0003-3369-2958"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Daniel Kressner","raw_affiliation_strings":["\u00c9cole Polytechnique, F\u00e9d\u00e9rale de Lausanne#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique, F\u00e9d\u00e9rale de Lausanne#TAB#","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039297086","display_name":"Bart Vandereycken","orcid":"https://orcid.org/0000-0002-6501-816X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bart Vandereycken","raw_affiliation_strings":["Princeton University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5072,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.96217361,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"1","first_page":"292","last_page":"313"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9969000220298767,"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/krylov-subspace","display_name":"Krylov subspace","score":0.7740098237991333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7415127754211426},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6407607793807983},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5658177733421326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5597941875457764},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.48623886704444885},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.48226672410964966},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4484829008579254},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43515104055404663},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4201202392578125},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.4148826599121094},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.40838736295700073},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37605705857276917},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.326926052570343},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15613403916358948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0856526792049408}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7740098237991333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7415127754211426},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6407607793807983},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5658177733421326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5597941875457764},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.48623886704444885},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.48226672410964966},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4484829008579254},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43515104055404663},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4201202392578125},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.4148826599121094},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.40838736295700073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37605705857276917},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.326926052570343},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15613403916358948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0856526792049408},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/120869432","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120869432","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:oai:CiteSeerX.psu:10.1.1.381.3314","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.381.3314","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sam.math.ethz.ch/~kressner/pub/subspace_pseudospectrum.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:198547","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/198547","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:198547","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/198547","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W10078005","https://openalex.org/W25637881","https://openalex.org/W33466849","https://openalex.org/W149522324","https://openalex.org/W175988912","https://openalex.org/W1506690472","https://openalex.org/W1522512418","https://openalex.org/W1575147392","https://openalex.org/W1590577697","https://openalex.org/W1812003359","https://openalex.org/W1861644487","https://openalex.org/W1965683017","https://openalex.org/W1970944723","https://openalex.org/W1972112356","https://openalex.org/W1975277883","https://openalex.org/W1981265672","https://openalex.org/W1984560319","https://openalex.org/W1988732861","https://openalex.org/W1998990712","https://openalex.org/W2004162424","https://openalex.org/W2015320521","https://openalex.org/W2020884817","https://openalex.org/W2031328583","https://openalex.org/W2036808929","https://openalex.org/W2046164006","https://openalex.org/W2047917018","https://openalex.org/W2049041383","https://openalex.org/W2051601650","https://openalex.org/W2054155441","https://openalex.org/W2063904941","https://openalex.org/W2087462091","https://openalex.org/W2090963365","https://openalex.org/W2100004457","https://openalex.org/W2116753581","https://openalex.org/W2149454052","https://openalex.org/W2150200785","https://openalex.org/W2156291021","https://openalex.org/W2178909929","https://openalex.org/W2342316458","https://openalex.org/W2610857016","https://openalex.org/W3029645440"],"related_works":["https://openalex.org/W2042846224","https://openalex.org/W2358905935","https://openalex.org/W2942315554","https://openalex.org/W2804461272","https://openalex.org/W2040391781","https://openalex.org/W2375237787","https://openalex.org/W3134028852","https://openalex.org/W1930195566","https://openalex.org/W4287116713","https://openalex.org/W2164612684"],"abstract_inverted_index":{"The":[0],"pseudospectral":[1,47,69],"abscissa":[2,70],"and":[3,26,58,81,89,117],"the":[4,12,46,68,95,106,115,120],"stability":[5,13,107],"radius":[6],"are":[7],"well-established":[8],"tools":[9],"for":[10,44],"quantifying":[11],"of":[14,71,94,111,119],"a":[15,39,72],"matrix":[16,75],"under":[17],"unstructured":[18],"perturbations.":[19],"Based":[20],"on":[21],"first-order":[22],"eigenvalue":[23],"expansions,":[24],"Guglielmi":[25],"Overton":[27],"[SIAM":[28],"J.":[29],"Matrix":[30],"Anal.":[31],"Appl.,":[32],"32":[33],"(2011),":[34],"pp.":[35],"1166--1192]":[36],"recently":[37],"proposed":[38],"linearly":[40],"converging":[41],"iterative":[42],"method":[43,57],"computing":[45,105],"abscissa.":[48],"In":[49],"this":[50,56],"paper,":[51],"we":[52],"propose":[53],"to":[54,104],"combine":[55],"its":[59],"variants":[60],"with":[61],"subspace":[62,97,121],"acceleration.":[63],"Each":[64],"extraction":[65],"step":[66],"computes":[67],"small":[73],"rectangular":[74],"pencil,":[76],"which":[77],"is":[78],"comparably":[79],"cheap":[80],"guarantees":[82],"monotonicity.":[83],"We":[84],"observe":[85],"local":[86,91],"quadratic":[87],"convergence":[88,93],"prove":[90],"superlinear":[92],"resulting":[96],"methods.":[98,122],"Moreover,":[99],"these":[100],"methods":[101],"extend":[102],"naturally":[103],"radius.":[108],"A":[109],"number":[110],"numerical":[112],"experiments":[113],"demonstrate":[114],"robustness":[116],"efficiency":[118]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"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"}
