{"id":"https://openalex.org/W1964067206","doi":"https://doi.org/10.1137/130925621","title":"Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Hermitian and Related Structures","display_name":"Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Hermitian and Related Structures","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1964067206","doi":"https://doi.org/10.1137/130925621","mag":"1964067206"},"language":"en","primary_location":{"id":"doi:10.1137/130925621","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130925621","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/A5088313330","display_name":"Shreemayee Bora","orcid":"https://orcid.org/0000-0002-0021-1591"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shreemayee Bora","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009600305","display_name":"Michael Karow","orcid":"https://orcid.org/0000-0002-3582-1488"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Karow","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103132248","display_name":"Christian Mehl","orcid":"https://orcid.org/0000-0003-2146-4974"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Mehl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003219051","display_name":"Punit Sharma","orcid":"https://orcid.org/0000-0001-5110-4449"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Punit Sharma","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5088313330"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5591,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.8876171,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"2","first_page":"453","last_page":"475"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8896424770355225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8533398509025574},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.788571834564209},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.7740564346313477},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.618775486946106},{"id":"https://openalex.org/keywords/hermitian-function","display_name":"Hermitian function","score":0.5381470918655396},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5162465572357178},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.48370224237442017},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.44150158762931824},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4296191334724426},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.41453635692596436},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4001879096031189},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3817816972732544}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8896424770355225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8533398509025574},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.788571834564209},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.7740564346313477},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.618775486946106},{"id":"https://openalex.org/C146783285","wikidata":"https://www.wikidata.org/wiki/Q3236862","display_name":"Hermitian function","level":3,"score":0.5381470918655396},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5162465572357178},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.48370224237442017},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.44150158762931824},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4296191334724426},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.41453635692596436},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4001879096031189},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3817816972732544},{"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130925621","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130925621","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:doi:10.14279/depositonce-6552","is_oa":false,"landing_page_url":"https://depositonce.tu-berlin.de/handle/11303/7279","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"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":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1225265921","https://openalex.org/W1965573117","https://openalex.org/W1970606629","https://openalex.org/W1972317710","https://openalex.org/W1974756711","https://openalex.org/W1991026314","https://openalex.org/W2000913668","https://openalex.org/W2002497815","https://openalex.org/W2015155239","https://openalex.org/W2015321063","https://openalex.org/W2016127945","https://openalex.org/W2044008067","https://openalex.org/W2052296591","https://openalex.org/W2067832305","https://openalex.org/W2094122256","https://openalex.org/W2101666264","https://openalex.org/W2108754424","https://openalex.org/W2117870622","https://openalex.org/W2123022662","https://openalex.org/W2132177635","https://openalex.org/W2139529710"],"related_works":["https://openalex.org/W2047937394","https://openalex.org/W1489986405","https://openalex.org/W2330447052","https://openalex.org/W4387938021","https://openalex.org/W2016290153","https://openalex.org/W2143986475","https://openalex.org/W2100313195","https://openalex.org/W4206014518","https://openalex.org/W4244361680","https://openalex.org/W2090623183"],"abstract_inverted_index":{"We":[0],"derive":[1],"a":[2,9,20,61],"formula":[3],"for":[4,36],"the":[5,65],"backward":[6,66],"error":[7],"of":[8,19,39],"complex":[10],"number":[11],"$\\lambda$":[12],"when":[13],"considered":[14],"as":[15],"an":[16],"approximate":[17,37],"eigenvalue":[18],"Hermitian":[21,29],"matrix":[22,40],"pencil":[23],"or":[24],"polynomial":[25],"with":[26,44,68,77],"respect":[27,69,78],"to":[28,70,79],"perturbations.":[30,81],"The":[31],"same":[32],"are":[33],"also":[34],"obtained":[35],"eigenvalues":[38],"pencils":[41],"and":[42,50,75],"polynomials":[43],"related":[45],"structures":[46],"like":[47],"skew-Hermitian,":[48],"$*$-even,":[49],"$*$-odd.":[51],"Numerical":[52],"experiments":[53],"suggest":[54],"that":[55,72],"in":[56],"many":[57],"cases":[58],"there":[59],"is":[60],"significant":[62],"difference":[63],"between":[64],"errors":[67],"perturbations":[71],"preserve":[73],"structure":[74],"those":[76],"arbitrary":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}