{"id":"https://openalex.org/W2060198758","doi":"https://doi.org/10.1109/tsp.2014.2367460","title":"Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices","display_name":"Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices","publication_year":2014,"publication_date":"2014-11-04","ids":{"openalex":"https://openalex.org/W2060198758","doi":"https://doi.org/10.1109/tsp.2014.2367460","mag":"2060198758"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2014.2367460","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2014.2367460","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://strathprints.strath.ac.uk/50762/1/Redif_etal_IEEETSP_2015_Sequential_matrix_diagonalization_algorithms.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075426985","display_name":"Soydan Redif","orcid":"https://orcid.org/0000-0003-4325-1080"},"institutions":[{"id":"https://openalex.org/I116528569","display_name":"European University of Lefke","ror":"https://ror.org/00t7bpe49","country_code":"TR","type":"education","lineage":["https://openalex.org/I116528569"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Soydan Redif","raw_affiliation_strings":["Electrical and Electronic Engineering Department, European University of Lefke, Gemikonagi, Turkey","[Electrical and Electronic Engineering Department, European University of Lefke, Gemikonagi, Turkey]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic Engineering Department, European University of Lefke, Gemikonagi, Turkey","institution_ids":["https://openalex.org/I116528569"]},{"raw_affiliation_string":"[Electrical and Electronic Engineering Department, European University of Lefke, Gemikonagi, Turkey]","institution_ids":["https://openalex.org/I116528569"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045197736","display_name":"Stephan Weiss","orcid":"https://orcid.org/0000-0002-3486-7206"},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stephan Weiss","raw_affiliation_strings":["Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow, Scotland","[Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow, Scotland]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow, Scotland","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"[Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow, Scotland]","institution_ids":["https://openalex.org/I181647926"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105458070","display_name":"J.G. McWhirter","orcid":"https://orcid.org/0000-0003-1810-3318"},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"John G. McWhirter","raw_affiliation_strings":["Cardiff University, Cardiff, UK","Cardiff University, Cardiff, Wales, UK;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cardiff University, Cardiff, UK","institution_ids":["https://openalex.org/I79510175"]},{"raw_affiliation_string":"Cardiff University, Cardiff, Wales, UK;","institution_ids":["https://openalex.org/I79510175"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.615,"has_fulltext":true,"cited_by_count":116,"citation_normalized_percentile":{"value":0.98778469,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"63","issue":"1","first_page":"81","last_page":"89"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9979000091552734,"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/T11946","display_name":"Antenna Design and Optimization","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/matrix-polynomial","display_name":"Matrix polynomial","score":0.7100170254707336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7058770656585693},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.6903666257858276},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.615458071231842},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5923527479171753},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5489247441291809},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5259081125259399},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5136205554008484},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.49307963252067566},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.47926828265190125},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4329657554626465},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.42344731092453003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37667015194892883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33848637342453003}],"concepts":[{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.7100170254707336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7058770656585693},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.6903666257858276},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.615458071231842},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5923527479171753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5489247441291809},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5259081125259399},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5136205554008484},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.49307963252067566},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.47926828265190125},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4329657554626465},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.42344731092453003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37667015194892883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33848637342453003},{"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/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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2014.2367460","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2014.2367460","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:http://orca.cardiff.ac.uk:68978","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:strathprints.strath.ac.uk:50762","is_oa":true,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/70486.html>","pdf_url":"https://strathprints.strath.ac.uk/50762/1/Redif_etal_IEEETSP_2015_Sequential_matrix_diagonalization_algorithms.pdf","source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"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":"PeerReviewed"}],"best_oa_location":{"id":"pmh:oai:strathprints.strath.ac.uk:50762","is_oa":true,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/70486.html>","pdf_url":"https://strathprints.strath.ac.uk/50762/1/Redif_etal_IEEETSP_2015_Sequential_matrix_diagonalization_algorithms.pdf","source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"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":"PeerReviewed"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6143932528","display_name":null,"funder_award_id":"EP/K014307","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6485023388","display_name":"Signal Processing Solutions for the Networked Battlespace","funder_award_id":"EP/K014307/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7219166536","display_name":null,"funder_award_id":"EP/K014307/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2060198758.pdf","grobid_xml":"https://content.openalex.org/works/W2060198758.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W599608442","https://openalex.org/W1481646516","https://openalex.org/W1491427864","https://openalex.org/W1508642566","https://openalex.org/W1667165204","https://openalex.org/W1871872530","https://openalex.org/W2021964357","https://openalex.org/W2025032488","https://openalex.org/W2033128271","https://openalex.org/W2035984194","https://openalex.org/W2039465757","https://openalex.org/W2072656871","https://openalex.org/W2075081148","https://openalex.org/W2095706820","https://openalex.org/W2116701188","https://openalex.org/W2135669535","https://openalex.org/W2136126519","https://openalex.org/W2147792942","https://openalex.org/W2154776657","https://openalex.org/W2159211918","https://openalex.org/W2162459359","https://openalex.org/W2165682245","https://openalex.org/W2620801485","https://openalex.org/W2798813531","https://openalex.org/W2798909945","https://openalex.org/W3133563580","https://openalex.org/W6629231215","https://openalex.org/W6683034992","https://openalex.org/W6738192120"],"related_works":["https://openalex.org/W1489986405","https://openalex.org/W2382784327","https://openalex.org/W2140446896","https://openalex.org/W2335071938","https://openalex.org/W2023818677","https://openalex.org/W1973507931","https://openalex.org/W2150953077","https://openalex.org/W2144948711","https://openalex.org/W2150994185","https://openalex.org/W2060198758"],"abstract_inverted_index":{"For":[0],"parahermitian":[1],"polynomial":[2,28,62],"matrices,":[3],"which":[4],"can":[5,23],"be":[6,24],"used,":[7],"for":[8],"example,":[9],"to":[10,26,64],"characterize":[11],"space-time":[12],"covariance":[13],"in":[14],"broadband":[15],"array":[16],"processing,":[17],"the":[18,51,55,61,65,71],"conventional":[19],"eigenvalue":[20],"decomposition":[21],"(EVD)":[22],"generalized":[25],"a":[27,35],"matrix":[29,43,63],"EVD":[30],"(PEVD).":[31],"In":[32],"this":[33],"paper,":[34],"new":[36],"iterative":[37],"PEVD":[38,97],"algorithm":[39,53],"based":[40],"on":[41],"sequential":[42],"diagonalization":[44,88],"(SMD)":[45],"is":[46,79,83],"introduced.":[47],"At":[48],"every":[49],"step":[50],"SMD":[52,86],"shifts":[54],"dominant":[56],"column":[57],"or":[58],"row":[59],"of":[60,77],"zero":[66],"lag":[67],"position":[68],"and":[69,81,90],"eliminates":[70],"resulting":[72],"instantaneous":[73],"correlation.":[74],"A":[75],"proof":[76],"convergence":[78],"provided,":[80],"it":[82],"demonstrated":[84],"that":[85],"establishes":[87],"faster":[89],"with":[91],"lower":[92],"order":[93],"operations":[94],"than":[95],"existing":[96],"algorithms.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}