{"id":"https://openalex.org/W4296079431","doi":"https://doi.org/10.1109/tsp.2022.3207291","title":"The Fixed Point Iteration of Positive Concave Mappings Converges Geometrically if a Fixed Point Exists: Implications to Wireless Systems","display_name":"The Fixed Point Iteration of Positive Concave Mappings Converges Geometrically if a Fixed Point Exists: Implications to Wireless Systems","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4296079431","doi":"https://doi.org/10.1109/tsp.2022.3207291"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2022.3207291","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2022.3207291","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/A5047411328","display_name":"Tomasz Piotrowski","orcid":"https://orcid.org/0000-0002-1998-4658"},"institutions":[{"id":"https://openalex.org/I2800274787","display_name":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute","ror":"https://ror.org/02tbr6331","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2800274787","https://openalex.org/I4923324"]},{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["DE","PL"],"is_corresponding":true,"raw_author_name":"Tomasz Piotrowski","raw_affiliation_strings":["Faculty of Physics, Astronomy and Applied Informatics, Nicolaus Copernicus University, Torun, Poland","Fraunhofer Heinrich Hertz Institute Einsteinufer 37, 10587 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Astronomy and Applied Informatics, Nicolaus Copernicus University, Torun, Poland","institution_ids":["https://openalex.org/I3019271933"]},{"raw_affiliation_string":"Fraunhofer Heinrich Hertz Institute Einsteinufer 37, 10587 Berlin, Germany","institution_ids":["https://openalex.org/I2800274787"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082367041","display_name":"Renato L. G. Cavalcante","orcid":"https://orcid.org/0000-0002-8826-7580"},"institutions":[{"id":"https://openalex.org/I2800274787","display_name":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute","ror":"https://ror.org/02tbr6331","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2800274787","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Renato Luis Garrido Cavalcante","raw_affiliation_strings":["Fraunhofer Heinrich Hertz Institute, Berlin, Germany","Fraunhofer Heinrich Hertz Institute Einsteinufer 37, 10587 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Heinrich Hertz Institute, Berlin, Germany","institution_ids":["https://openalex.org/I2800274787"]},{"raw_affiliation_string":"Fraunhofer Heinrich Hertz Institute Einsteinufer 37, 10587 Berlin, Germany","institution_ids":["https://openalex.org/I2800274787"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047411328"],"corresponding_institution_ids":["https://openalex.org/I2800274787","https://openalex.org/I3019271933"],"apc_list":null,"apc_paid":null,"fwci":0.8312,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71337208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"70","issue":null,"first_page":"4697","last_page":"4710"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.8441284894943237},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.7384263277053833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6892232894897461},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"Fixed-point iteration","score":0.6254626512527466},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5813989639282227},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44357264041900635},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4320460855960846},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.353029727935791},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3488197326660156},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2796945571899414}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.8441284894943237},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.7384263277053833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6892232894897461},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.6254626512527466},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5813989639282227},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44357264041900635},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4320460855960846},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.353029727935791},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3488197326660156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2796945571899414},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2022.3207291","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2022.3207291","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:null:publica/443227","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/443227","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335039","display_name":"Narodowe Centrum Bada\u0144 i Rozwoju","ror":"https://ror.org/05pwfyy15"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W562922095","https://openalex.org/W639883061","https://openalex.org/W1608548244","https://openalex.org/W1848804074","https://openalex.org/W1968669685","https://openalex.org/W1989689783","https://openalex.org/W1998520172","https://openalex.org/W1999781352","https://openalex.org/W2046124468","https://openalex.org/W2059338174","https://openalex.org/W2074030544","https://openalex.org/W2077925014","https://openalex.org/W2081641166","https://openalex.org/W2096102595","https://openalex.org/W2116407052","https://openalex.org/W2127756703","https://openalex.org/W2149627282","https://openalex.org/W2164271287","https://openalex.org/W2164710299","https://openalex.org/W2208336411","https://openalex.org/W2228820242","https://openalex.org/W2406356325","https://openalex.org/W2431771009","https://openalex.org/W2486208190","https://openalex.org/W2503112372","https://openalex.org/W2595897327","https://openalex.org/W2898569439","https://openalex.org/W2925232796","https://openalex.org/W2938535929","https://openalex.org/W2963499342","https://openalex.org/W2979337770","https://openalex.org/W3031029555","https://openalex.org/W3083329435","https://openalex.org/W3091729653","https://openalex.org/W3102647677","https://openalex.org/W3193922030","https://openalex.org/W4287109918","https://openalex.org/W4299512035","https://openalex.org/W6839926931"],"related_works":["https://openalex.org/W2090103360","https://openalex.org/W2122094047","https://openalex.org/W2147776645","https://openalex.org/W399006150","https://openalex.org/W2049306475","https://openalex.org/W4292324088","https://openalex.org/W2027835668","https://openalex.org/W2997140122","https://openalex.org/W2403877097","https://openalex.org/W3032898267"],"abstract_inverted_index":{"We":[0,23],"prove":[1],"that":[2,26,129],"the":[3,36,50,58,103,111],"fixed":[4,14,82,99],"point":[5,15,83,100],"iteration":[6],"of":[7,38,42,57,80,102,106,113],"arbitrary":[8],"positive":[9],"concave":[10],"mappings":[11,44],"with":[12,47],"nonempty":[13],"set":[16],"converges":[17],"geometrically":[18],"for":[19,30],"any":[20],"starting":[21],"point.":[22],"also":[24],"show":[25],"positivity":[27],"is":[28],"crucial":[29],"this":[31],"result":[32],"to":[33],"hold,":[34],"and":[35,69],"concept":[37],"(nonlinear)":[39],"spectral":[40],"radius":[41],"asymptotic":[43],"provides":[45],"us":[46],"information":[48],"about":[49],"convergence":[51,88,115],"factor.":[52],"As":[53],"a":[54,81],"practical":[55],"implication":[56],"results":[59],"shown":[60,86],"here,":[61],"we":[62],"rigorously":[63],"explain":[64],"why":[65],"some":[66],"power":[67],"control":[68],"load":[70],"estimation":[71],"algorithms":[72,92],"in":[73,89,122,126],"wireless":[74],"networks,":[75],"which":[76],"are":[77,130],"particular":[78],"instances":[79],"iteration,":[84],"have":[85,93],"geometric":[87],"simulations.":[90],"These":[91],"been":[94],"typically":[95],"derived":[96],"by":[97],"considering":[98],"iterations":[101],"general":[104],"class":[105],"standard":[107],"interference":[108],"mappings,":[109],"so":[110],"possibility":[112],"sublinear":[114],"rate":[116],"could":[117],"not":[118],"be":[119],"ruled":[120],"out":[121],"previous":[123],"studies,":[124],"except":[125],"special":[127],"cases":[128],"often":[131],"more":[132],"restrictive":[133],"than":[134],"those":[135],"considered":[136],"here.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}