{"id":"https://openalex.org/W2121661590","doi":"https://doi.org/10.1109/tsp.2012.2186447","title":"Sampling Uniformly From the Set of Positive Definite Matrices With Trace Constraint","display_name":"Sampling Uniformly From the Set of Positive Definite Matrices With Trace Constraint","publication_year":2012,"publication_date":"2012-02-01","ids":{"openalex":"https://openalex.org/W2121661590","doi":"https://doi.org/10.1109/tsp.2012.2186447","mag":"2121661590"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2186447","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2186447","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103089220","display_name":"Martin Mittelbach","orcid":"https://orcid.org/0000-0001-6219-6967"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Mittelbach","raw_affiliation_strings":["Communications Theory, Communications Laboratory, Dresden University of Technology, Dresden, Germany","Commun. Lab., Dresden Univ. of Technol., Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communications Theory, Communications Laboratory, Dresden University of Technology, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]},{"raw_affiliation_string":"Commun. Lab., Dresden Univ. of Technol., Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058121440","display_name":"Bho Matthiesen","orcid":"https://orcid.org/0000-0002-4582-3938"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bho Matthiesen","raw_affiliation_strings":["Communications Theory, Communications Laboratory, Dresden University of Technology, Dresden, Germany","Commun. Lab., Dresden Univ. of Technol., Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communications Theory, Communications Laboratory, Dresden University of Technology, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]},{"raw_affiliation_string":"Commun. Lab., Dresden Univ. of Technol., Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029956964","display_name":"Eduard A. Jorswieck","orcid":"https://orcid.org/0000-0001-7893-8435"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Eduard A. Jorswieck","raw_affiliation_strings":["Communications Theory, Communications Laboratory, Dresden University of Technology, Dresden, Germany","Commun. Lab., Dresden Univ. of Technol., Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communications Theory, Communications Laboratory, Dresden University of Technology, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]},{"raw_affiliation_string":"Commun. Lab., Dresden Univ. of Technol., Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78650965"],"apc_list":null,"apc_paid":null,"fwci":1.9478,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86845015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"60","issue":"5","first_page":"2167","last_page":"2179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"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":0.9983999729156494,"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":0.9980000257492065,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9890999794006348,"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/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.8282747268676758},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7522470951080322},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5650033950805664},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5636833906173706},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.542178750038147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5399816632270813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5025100708007812},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.486726313829422},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4239305257797241},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41865837574005127},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3711509108543396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35384654998779297},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08076721429824829}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.8282747268676758},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7522470951080322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5650033950805664},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5636833906173706},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.542178750038147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5399816632270813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5025100708007812},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.486726313829422},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4239305257797241},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41865837574005127},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3711509108543396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35384654998779297},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08076721429824829},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2012.2186447","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2186447","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W39337161","https://openalex.org/W391578156","https://openalex.org/W604181985","https://openalex.org/W1594563152","https://openalex.org/W1968078808","https://openalex.org/W1981663184","https://openalex.org/W1987302741","https://openalex.org/W2000295531","https://openalex.org/W2010963344","https://openalex.org/W2069239663","https://openalex.org/W2084045976","https://openalex.org/W2087691922","https://openalex.org/W2105147296","https://openalex.org/W2116753372","https://openalex.org/W2117395782","https://openalex.org/W2139794367","https://openalex.org/W2152828142","https://openalex.org/W2162370583","https://openalex.org/W2165943096","https://openalex.org/W2491143551","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W2504688771","https://openalex.org/W4255359805","https://openalex.org/W1482750774","https://openalex.org/W4315697090","https://openalex.org/W2002877864","https://openalex.org/W63685308","https://openalex.org/W2394244817","https://openalex.org/W2233293187","https://openalex.org/W2075453197","https://openalex.org/W2924783966"],"abstract_inverted_index":{"We":[0],"derive":[1],"a":[2,23,41,60,109],"parameterization":[3,20,65],"of":[4,68,83,91],"positive":[5,31],"definite":[6,32],"matrices":[7,33],"using":[8,50],"the":[9,19,51,72,89,98,106],"Cholesky":[10],"decomposition":[11],"in":[12,78,108],"combination":[13],"with":[14,34],"hyperspherical":[15],"coordinates.":[16],"Based":[17],"on":[18],"we":[21,45,95,129],"develop":[22],"simple":[24],"and":[25,54,85],"efficient":[26,48,120],"method":[27,53,100],"to":[28,40,104],"randomly":[29],"generate":[30],"constant":[35],"or":[36,58,119],"bounded":[37],"trace":[38],"according":[39],"uniform":[42],"distribution.":[43,62],"Further,":[44],"present":[46],"an":[47,92],"implementation":[49],"inversion":[52],"either":[55],"rejection":[56],"sampling":[57,74,99],"transforming":[59],"beta":[61],"The":[63],"matrix":[64],"might":[66],"be":[67,102],"independent":[69],"interest,":[70],"whereas":[71],"random":[73],"algorithm":[75,123],"finds":[76],"applications":[77],"Monte":[79],"Carlo":[80],"simulations,":[81],"testing":[82],"algorithms,":[84],"performance":[86],"studies.":[87],"With":[88],"help":[90],"abstract":[93],"example":[94],"describe":[96],"how":[97],"can":[101],"used":[103],"approximate":[105],"optimum":[107],"difficult,":[110],"e.g.,":[111],"nonconvex,":[112],"optimization":[113,122],"problem":[114],"for":[115],"which":[116],"no":[117],"solution":[118],"global":[121],"is":[124],"known.":[125],"In":[126],"this":[127],"paper":[128],"consider":[130],"real":[131],"as":[132,134],"well":[133],"complex":[135],"matrices.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2025-10-10T00:00:00"}
