{"id":"https://openalex.org/W2015089196","doi":"https://doi.org/10.1137/s0036142997327063","title":"A Note on the Spectra and Pseudospectra of Waveform Relaxation Operators for Linear Differential-Algebraic Equations","display_name":"A Note on the Spectra and Pseudospectra of Waveform Relaxation Operators for Linear Differential-Algebraic Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2015089196","doi":"https://doi.org/10.1137/s0036142997327063","mag":"2015089196"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142997327063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997327063","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5034372090","display_name":"Yao\u2010Lin Jiang","orcid":"https://orcid.org/0000-0002-5541-1136"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yao-Lin Jiang","raw_affiliation_strings":["Xi'an Jiaotong University"],"affiliations":[{"raw_affiliation_string":"Xi'an Jiaotong University","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109563803","display_name":"Omar Wing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omar Wing","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034372090"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":3.1652,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.92078153,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"1","first_page":"186","last_page":"201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9929999709129333,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9868000149726868,"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":0.834524929523468},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7229101657867432},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6514345407485962},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6094794273376465},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5533386468887329},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4898333251476288},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.47822850942611694},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.47176292538642883},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4660172760486603},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4438815116882324},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.41427159309387207},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36951613426208496},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22896546125411987},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07923325896263123},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.061056703329086304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.834524929523468},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7229101657867432},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6514345407485962},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6094794273376465},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5533386468887329},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4898333251476288},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47822850942611694},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.47176292538642883},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4660172760486603},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4438815116882324},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.41427159309387207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36951613426208496},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22896546125411987},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07923325896263123},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.061056703329086304},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142997327063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997327063","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300010471/11","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300010471/11&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W175988912","https://openalex.org/W590118243","https://openalex.org/W611479614","https://openalex.org/W1480422175","https://openalex.org/W1524259561","https://openalex.org/W1977208243","https://openalex.org/W2027726943","https://openalex.org/W2032428933","https://openalex.org/W2036597275","https://openalex.org/W2057752799","https://openalex.org/W2062543345","https://openalex.org/W2069665540","https://openalex.org/W2075151302","https://openalex.org/W2085385512","https://openalex.org/W2117919754","https://openalex.org/W2140779530"],"related_works":["https://openalex.org/W1974895211","https://openalex.org/W2176409448","https://openalex.org/W2129841057","https://openalex.org/W3040712279","https://openalex.org/W2364769705","https://openalex.org/W2056136368","https://openalex.org/W2374664672","https://openalex.org/W3100285276","https://openalex.org/W4297412021","https://openalex.org/W2212647145"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3],"derived":[4],"the":[5,8,43,54],"expressions":[6,25],"of":[7,12,21,28,30],"spectra":[9],"and":[10,32,42],"pseudospectra":[11],"waveform":[13],"relaxation":[14],"operators":[15],"for":[16],"general":[17],"linear":[18],"differential-algebraic":[19],"equations":[20],"index":[22],"one.":[23],"The":[24],"are":[26,50],"generalizations":[27],"those":[29],"Lumsdaine":[31],"Wu":[33],"(SIAM":[34],"J.":[35],"Sci.":[36],"Comput.,":[37],"18":[38],"(1997),":[39],"pp.":[40],"286--304)":[41],"derivation":[44],"here":[45],"is":[46],"nontrivial.":[47],"Numerical":[48],"experiments":[49],"given":[51],"to":[52],"verify":[53],"theoretical":[55],"results.":[56]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}