{"id":"https://openalex.org/W2028412357","doi":"https://doi.org/10.1137/0614052","title":"Approximation by a Hermitian Positive Semidefinite Toeplitz Matrix","display_name":"Approximation by a Hermitian Positive Semidefinite Toeplitz Matrix","publication_year":1993,"publication_date":"1993-07-01","ids":{"openalex":"https://openalex.org/W2028412357","doi":"https://doi.org/10.1137/0614052","mag":"2028412357"},"language":"en","primary_location":{"id":"doi:10.1137/0614052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614052","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/A5110022370","display_name":"T. J. Suffridge","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"T. J. Suffridge","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078083455","display_name":"T. L. Hayden","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. L. Hayden","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110022370"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.15781379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"3","first_page":"721","last_page":"734"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9958000183105469,"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":0.9958000183105469,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","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"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9783999919891357,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9411094188690186},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8877053260803223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.835541844367981},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6688618659973145},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6558840274810791},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5672358274459839},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5455933213233948},{"id":"https://openalex.org/keywords/levinson-recursion","display_name":"Levinson recursion","score":0.4947375953197479},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4405980706214905},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42396849393844604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3897792398929596},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3758532404899597},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35130172967910767},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1959439218044281},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18291988968849182}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9411094188690186},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8877053260803223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.835541844367981},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6688618659973145},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6558840274810791},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5672358274459839},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5455933213233948},{"id":"https://openalex.org/C122212055","wikidata":"https://www.wikidata.org/wiki/Q11679774","display_name":"Levinson recursion","level":3,"score":0.4947375953197479},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4405980706214905},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42396849393844604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3897792398929596},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3758532404899597},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35130172967910767},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1959439218044281},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18291988968849182},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0614052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614052","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":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1536329667","https://openalex.org/W1964922595","https://openalex.org/W1981467185","https://openalex.org/W1999640431","https://openalex.org/W2000389722","https://openalex.org/W2009950035","https://openalex.org/W2016425264","https://openalex.org/W2045463928","https://openalex.org/W2055610959","https://openalex.org/W2072863821","https://openalex.org/W4205212851"],"related_works":["https://openalex.org/W2045714585","https://openalex.org/W1987843132","https://openalex.org/W2374553943","https://openalex.org/W1654107233","https://openalex.org/W2182312572","https://openalex.org/W2361901126","https://openalex.org/W2070080181","https://openalex.org/W2015339619","https://openalex.org/W4237208466","https://openalex.org/W1826911152"],"abstract_inverted_index":{"The":[0],"problem":[1],"of":[2,15,46],"finding":[3],"the":[4,12,44],"nearest":[5],"Hermitian":[6],"positive":[7],"semidefinite":[8],"Toeplitz":[9],"matrix":[10,22],"(in":[11],"Frobenius":[13],"norm)":[14],"a":[16],"given":[17],"rank":[18],"to":[19,56],"an":[20],"arbitrary":[21],"is":[23],"considered.":[24],"A":[25,37],"special":[26],"orthogonal":[27],"basis":[28],"and":[29],"equally":[30],"spaced":[31],"frequencies":[32],"allow":[33],"good":[34],"initial":[35],"approximations.":[36],"second":[38],"method":[39],"using":[40],"alternating":[41],"projections":[42],"solves":[43],"case":[45],"unrestricted":[47],"rank.":[48],"Some":[49],"interesting":[50],"numerical":[51],"results":[52],"suggest":[53],"possible":[54],"applications":[55],"signal":[57],"processing":[58],"problems.":[59]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}