{"id":"https://openalex.org/W2529669714","doi":"https://doi.org/10.1137/16m107952x","title":"Criss-Cross Type Algorithms for Computing the Real Pseudospectral Abscissa","display_name":"Criss-Cross Type Algorithms for Computing the Real Pseudospectral Abscissa","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2529669714","doi":"https://doi.org/10.1137/16m107952x","mag":"2529669714"},"language":"en","primary_location":{"id":"doi:10.1137/16m107952x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m107952x","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/A5102002819","display_name":"Ding Lu","orcid":"https://orcid.org/0009-0009-5493-0696"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding Lu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039297086","display_name":"Bart Vandereycken","orcid":"https://orcid.org/0000-0002-6501-816X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bart Vandereycken","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":0.2393,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.52592708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":"3","first_page":"891","last_page":"923"},"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":0.9980000257492065,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"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/mathematics","display_name":"Mathematics","score":0.8243943452835083},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6301529407501221},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5676398277282715},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5171929597854614},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.47794321179389954},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4400427043437958},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.43915557861328125},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4369807541370392},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4243188202381134},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36298465728759766},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28466612100601196}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8243943452835083},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6301529407501221},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5676398277282715},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5171929597854614},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.47794321179389954},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4400427043437958},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.43915557861328125},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4369807541370392},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4243188202381134},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36298465728759766},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28466612100601196},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political 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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m107952x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m107952x","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":23,"referenced_works":["https://openalex.org/W149522324","https://openalex.org/W164439288","https://openalex.org/W175988912","https://openalex.org/W658559791","https://openalex.org/W1506690472","https://openalex.org/W1861644487","https://openalex.org/W1879276171","https://openalex.org/W1972112356","https://openalex.org/W1990838156","https://openalex.org/W1998990712","https://openalex.org/W2006017464","https://openalex.org/W2013853256","https://openalex.org/W2047917018","https://openalex.org/W2050649877","https://openalex.org/W2051800967","https://openalex.org/W2082864352","https://openalex.org/W2090832914","https://openalex.org/W2094607148","https://openalex.org/W2163044500","https://openalex.org/W2167193748","https://openalex.org/W2209535128","https://openalex.org/W2274016777","https://openalex.org/W2413150331"],"related_works":["https://openalex.org/W1637798125","https://openalex.org/W2367926634","https://openalex.org/W4366831400","https://openalex.org/W2158044763","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W3206304544","https://openalex.org/W3017414697","https://openalex.org/W2081240962","https://openalex.org/W2038812594"],"abstract_inverted_index":{"The":[0,24,34,111,149,159],"real":[1,5,14,35,43,61,75,93],"$\\varepsilon$-pseudospectrum":[2],"of":[3,9,12,45,58,91,163],"a":[4,49,68,88,130],"matrix":[6],"$A$":[7,59],"consists":[8],"the":[10,41,54,74,80,92,138,164],"eigenvalues":[11,47],"all":[13],"matrices":[15],"that":[16],"are":[17,167],"$\\varepsilon$-close":[18],"in":[19,29,134],"spectral":[20,30,81],"norm":[21],"to":[22,72,116,122,145,154],"$A$.":[23],"closeness":[25],"is":[26,40,85,114,152],"commonly":[27],"measured":[28],"or":[31],"Frobenius":[32],"norm.":[33,82],"pseudospectral":[36,76],"$\\varepsilon$-pseudospectral":[37,77],"abscissa,":[38],"which":[39,135],"largest":[42],"part":[44],"these":[46],"for":[48,79],"prescribed":[50],"value":[51,108],"$\\varepsilon$,":[52],"measures":[53],"structured":[55],"robust":[56],"stability":[57],"w.r.t.":[60],"perturbations.":[62],"In":[63],"this":[64],"paper,":[65],"we":[66,128,136],"introduce":[67],"criss-cross":[69,139],"type":[70],"algorithm":[71,84,113,140],"compute":[73],"abscissa":[78],"Our":[83],"based":[86],"on":[87,169],"superset":[89],"characterization":[90],"pseudospectrum":[94],"where":[95],"each":[96],"criss":[97],"and":[98,106,120,161],"cross":[99],"search":[100],"involves":[101],"solving":[102],"linear":[103],"eigenvalue":[104],"problems":[105],"singular":[107],"optimization":[109],"problems.":[110,148],"new":[112],"proved":[115,153],"be":[117,123,155],"globally":[118],"convergent,":[119],"observed":[121],"locally":[124,156],"linearly":[125],"convergent.":[126,158],"Moreover,":[127],"propose":[129],"subspace":[131,142,150],"projection":[132,143],"framework":[133],"combine":[137],"with":[141],"techniques":[144],"solve":[146],"large-scale":[147],"acceleration":[151],"superlinearly":[157],"robustness":[160],"efficiency":[162],"proposed":[165],"algorithms":[166],"demonstrated":[168],"numerical":[170],"examples.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}