{"id":"https://openalex.org/W1422451957","doi":"https://doi.org/10.1137/15m1006945","title":"Invariant Polytopes of Sets of Matrices with Application to Regularity of Wavelets and Subdivisions","display_name":"Invariant Polytopes of Sets of Matrices with Application to Regularity of Wavelets and Subdivisions","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1422451957","doi":"https://doi.org/10.1137/15m1006945","mag":"1422451957"},"language":"en","primary_location":{"id":"doi:10.1137/15m1006945","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1006945","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/A5030219464","display_name":"Nicola Guglielmi","orcid":"https://orcid.org/0000-0003-3795-5225"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":["University of L'Aquila"],"affiliations":[{"raw_affiliation_string":"University of L'Aquila","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016511187","display_name":"Vladimir Yu. Protasov","orcid":"https://orcid.org/0000-0003-1862-2046"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vladimir Yu. Protasov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030219464"],"corresponding_institution_ids":["https://openalex.org/I26415053"],"apc_list":null,"apc_paid":null,"fwci":2.1602,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.84900464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"18","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9818000197410583,"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/mathematics","display_name":"Mathematics","score":0.8560061454772949},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6947888135910034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.513263463973999},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5074946284294128},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5008220672607422},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.48170095682144165},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.47816070914268494},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4623713493347168},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.45050907135009766},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4257574677467346},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.41525381803512573},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3782939910888672},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34069231152534485},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.33013641834259033},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2597673237323761}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8560061454772949},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6947888135910034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.513263463973999},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5074946284294128},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5008220672607422},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.48170095682144165},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.47816070914268494},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4623713493347168},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.45050907135009766},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4257574677467346},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.41525381803512573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3782939910888672},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34069231152534485},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33013641834259033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2597673237323761},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","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/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1006945","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1006945","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":[],"awards":[{"id":"https://openalex.org/G7600355076","display_name":null,"funder_award_id":"13-01-00642","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G7729054605","display_name":null,"funder_award_id":"14-01-00332","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320321648","display_name":"Dynasty Foundation","ror":"https://ror.org/044hrt695"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W55797859","https://openalex.org/W139997242","https://openalex.org/W658559791","https://openalex.org/W1642990561","https://openalex.org/W1973758855","https://openalex.org/W1980368307","https://openalex.org/W1980695038","https://openalex.org/W1991656001","https://openalex.org/W2003950764","https://openalex.org/W2008442517","https://openalex.org/W2015328669","https://openalex.org/W2019113134","https://openalex.org/W2020979852","https://openalex.org/W2030934791","https://openalex.org/W2032326995","https://openalex.org/W2032880693","https://openalex.org/W2035314514","https://openalex.org/W2039057583","https://openalex.org/W2040235632","https://openalex.org/W2046153167","https://openalex.org/W2051710605","https://openalex.org/W2055472587","https://openalex.org/W2060886109","https://openalex.org/W2065661959","https://openalex.org/W2072595795","https://openalex.org/W2082419392","https://openalex.org/W2095665834","https://openalex.org/W2098678476","https://openalex.org/W2098914003","https://openalex.org/W2118863844","https://openalex.org/W2121284344","https://openalex.org/W2133763708","https://openalex.org/W2142181992","https://openalex.org/W2144829110","https://openalex.org/W2338734304","https://openalex.org/W2341241031","https://openalex.org/W2376761670","https://openalex.org/W2798909945","https://openalex.org/W2911681356","https://openalex.org/W4251619700","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W4280529077","https://openalex.org/W1990363280","https://openalex.org/W4205312897","https://openalex.org/W2795347481","https://openalex.org/W2750153370","https://openalex.org/W1106115901","https://openalex.org/W2140072033"],"abstract_inverted_index":{"We":[0],"generalize":[1],"the":[2,9,27,46,63,66,75,85,105],"recent":[3],"invariant":[4],"polytope":[5],"algorithm":[6,28,47],"for":[7,70],"computing":[8],"joint":[10],"spectral":[11],"radius":[12],"and":[13,92],"extend":[14],"it":[15],"to":[16,30],"a":[17],"wider":[18],"class":[19],"of":[20,32,43,45,65,108,111],"matrix":[21],"sets.":[22],"This,":[23],"in":[24],"particular,":[25],"makes":[26],"applicable":[29],"sets":[31],"matrices":[33],"that":[34,84],"have":[35],"finitely":[36],"many":[37],"spectrum":[38],"maximizing":[39],"products.":[40],"A":[41],"criterion":[42],"convergence":[44],"is":[48,95],"proved.":[49],"As":[50],"an":[51],"application":[52],"we":[53,61,82,103],"solve":[54],"two":[55],"challenging":[56],"computational":[57],"open":[58],"problems.":[59],"First":[60],"find":[62],"regularity":[64],"Butterfly":[67],"subdivision":[68],"scheme":[69],"various":[71],"parameters":[72],"$\\omega$.":[73],"In":[74],"\u201cmost":[76],"regular\u201d":[77],"case":[78],"$\\omega":[79],"=":[80],"\\frac{1}{16}$,":[81],"prove":[83],"limit":[86],"function":[87],"has":[88],"H\u00f6lder":[89,106],"exponent":[90,107],"2":[91],"its":[93],"derivative":[94],"\u201calmost":[96],"Lipschitz\u201d":[97],"with":[98],"logarithmic":[99],"factor":[100],"2.":[101],"Second":[102],"compute":[104],"Daubechies":[109],"wavelets":[110],"high":[112],"order.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
