{"id":"https://openalex.org/W1977208243","doi":"https://doi.org/10.1137/s1064827594276035","title":"Computation of Pseudospectra by Continuation","display_name":"Computation of Pseudospectra by Continuation","publication_year":1997,"publication_date":"1997-03-01","ids":{"openalex":"https://openalex.org/W1977208243","doi":"https://doi.org/10.1137/s1064827594276035","mag":"1977208243"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827594276035","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827594276035","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5003813327","display_name":"S. H. Lui","orcid":"https://orcid.org/0000-0003-2024-5817"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. H. Lui","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003813327"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.6879,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.96164082,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"2","first_page":"565","last_page":"573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9940000176429749,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/continuation","display_name":"Continuation","score":0.7808024287223816},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.73487788438797},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7302026748657227},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7163391709327698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7113586664199829},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6388988494873047},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6155350208282471},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5929110646247864},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.4141533374786377},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3810250163078308},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27887850999832153},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.218292236328125}],"concepts":[{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.7808024287223816},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.73487788438797},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7302026748657227},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7163391709327698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7113586664199829},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6388988494873047},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6155350208282471},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5929110646247864},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4141533374786377},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3810250163078308},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27887850999832153},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.218292236328125},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827594276035","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827594276035","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":12,"referenced_works":["https://openalex.org/W1974943103","https://openalex.org/W1985532668","https://openalex.org/W2010913194","https://openalex.org/W2038516800","https://openalex.org/W2039393654","https://openalex.org/W2059685595","https://openalex.org/W2069195908","https://openalex.org/W2080634148","https://openalex.org/W2098533238","https://openalex.org/W2117949169","https://openalex.org/W2137029533","https://openalex.org/W2140153041"],"related_works":["https://openalex.org/W2102181290","https://openalex.org/W4365788292","https://openalex.org/W1976060951","https://openalex.org/W2083748498","https://openalex.org/W2049453722","https://openalex.org/W1521926466","https://openalex.org/W2103502297","https://openalex.org/W2484275557","https://openalex.org/W2511980821","https://openalex.org/W1977208243"],"abstract_inverted_index":{"The":[0,44],"concept":[1],"of":[2,12,23,53,69,72],"pseudospectrum":[3],"was":[4],"introduced":[5],"by":[6,33,40],"Trefethen":[7],"to":[8,47,66],"explain":[9],"the":[10,42,54],"behavior":[11],"nonnormal":[13],"operators.":[14],"Many":[15],"phenomena":[16],"(for":[17],"example,":[18],"hydrodynamic":[19],"instability":[20],"and":[21],"convergence":[22],"iterative":[24],"methods":[25,65],"for":[26,32],"linear":[27],"systems)":[28],"cannot":[29],"be":[30],"accounted":[31],"eigenvalue":[34],"analysis":[35],"but":[36],"are":[37],"more":[38],"understandable":[39],"examining":[41],"pseudospectra.":[43],"straightforward":[45],"way":[46],"compute":[48],"pseudospectra":[49,68],"involves":[50],"many":[51],"applications":[52],"singular":[55],"value":[56],"decomposition":[57],"(SVD).":[58],"This":[59],"paper":[60],"presents":[61],"several":[62],"fast":[63],"continuation":[64],"calculate":[67],"different":[70],"types":[71],"matrices.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
