{"id":"https://openalex.org/W2031051813","doi":"https://doi.org/10.1515/156939506776382148","title":"Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem","display_name":"Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2031051813","doi":"https://doi.org/10.1515/156939506776382148","mag":"2031051813"},"language":"en","primary_location":{"id":"doi:10.1515/156939506776382148","is_oa":false,"landing_page_url":"https://doi.org/10.1515/156939506776382148","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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/A5002577873","display_name":"Suliman Al\u2010Homidan","orcid":"https://orcid.org/0000-0002-5998-0635"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"S. Al-Homidan","raw_affiliation_strings":["Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, PO Box 119, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, PO Box 119, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002577873"],"corresponding_institution_ids":["https://openalex.org/I134085113"],"apc_list":null,"apc_paid":null,"fwci":0.3704,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64029371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"1","first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973999857902527,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8444926738739014},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7963219881057739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7632790803909302},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.7151728868484497},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.5616792440414429},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.552028477191925},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4991142749786377},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.4762035608291626},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.4714178740978241},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45968788862228394},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4299512505531311},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41686758399009705},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31469929218292236},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.1684841513633728},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1251671314239502},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07643121480941772},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07205364108085632}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8444926738739014},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7963219881057739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7632790803909302},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.7151728868484497},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.5616792440414429},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.552028477191925},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4991142749786377},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.4762035608291626},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.4714178740978241},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45968788862228394},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4299512505531311},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41686758399009705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31469929218292236},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.1684841513633728},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1251671314239502},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07643121480941772},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07205364108085632},{"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/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/156939506776382148","is_oa":false,"landing_page_url":"https://doi.org/10.1515/156939506776382148","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1550404336","https://openalex.org/W1632601927","https://openalex.org/W1999913571","https://openalex.org/W2012110988","https://openalex.org/W2014839543","https://openalex.org/W2016425264","https://openalex.org/W2028412357","https://openalex.org/W2077274614","https://openalex.org/W2091889437","https://openalex.org/W2094136786","https://openalex.org/W2098271112","https://openalex.org/W2105235982","https://openalex.org/W2119080913","https://openalex.org/W2169872334","https://openalex.org/W2490314302","https://openalex.org/W2495457432","https://openalex.org/W2912522929","https://openalex.org/W4200283578","https://openalex.org/W4205212851"],"related_works":["https://openalex.org/W2036562274","https://openalex.org/W2121045497","https://openalex.org/W2269291726","https://openalex.org/W4232508221","https://openalex.org/W4231773446","https://openalex.org/W2128202699","https://openalex.org/W2531901171","https://openalex.org/W1985090152","https://openalex.org/W2617248812","https://openalex.org/W1500263762"],"abstract_inverted_index":{"The":[0],"nearest":[1],"positive":[2],"semidefinite":[3,53,63],"symmetric":[4],"Toeplitz":[5],"matrix":[6,12],"to":[7,40],"an":[8],"arbitrary":[9],"data":[10],"covariance":[11],"is":[13],"useful":[14],"in":[15],"many":[16],"areas":[17],"of":[18,60,74],"engineering,":[19],"including":[20],"stochastic":[21],"filtering":[22],"and":[23,64],"digital":[24],"signal":[25],"processing":[26],"applications.":[27],"In":[28],"this":[29],"paper,":[30],"the":[31,58,72,78],"interior":[32],"point":[33],"primal-dual":[34],"path-following":[35],"method":[36,82],"will":[37,83],"be":[38,84],"used":[39],"solve":[41],"our":[42],"problem":[43],"after":[44],"reformulating":[45],"it":[46],"into":[47,57],"different":[48],"forms,":[49],"first":[50],"as":[51],"a":[52,61],"programming":[54],"problem,":[55],"then":[56],"form":[59],"mixed":[62],"second-order":[65],"cone":[66],"optimization":[67],"problem.":[68],"Numerical":[69],"results,":[70],"comparing":[71],"performance":[73],"these":[75],"methods":[76],"against":[77],"modified":[79],"alternating":[80],"projection":[81],"reported.":[85]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}