{"id":"https://openalex.org/W1942047793","doi":"https://doi.org/10.1137/151006159","title":"Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure","display_name":"Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1942047793","doi":"https://doi.org/10.1137/151006159","mag":"1942047793"},"language":"en","primary_location":{"id":"doi:10.1137/151006159","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151006159","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11384/75248","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053109099","display_name":"Michele Benzi","orcid":"https://orcid.org/0000-0001-6099-0294"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michele Benzi","raw_affiliation_strings":["Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081841768","display_name":"Valeria Simoncini","orcid":"https://orcid.org/0000-0003-0795-5865"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Valeria Simoncini","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Bologna,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Bologna,","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053109099"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":7.2683,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.97534548,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"36","issue":"3","first_page":"1263","last_page":"1282"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9977999925613403,"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/kronecker-delta","display_name":"Kronecker delta","score":0.8934028148651123},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8130024671554565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8029608726501465},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6653523445129395},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.5698402523994446},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5482174158096313},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5392808318138123},{"id":"https://openalex.org/keywords/matrix-analysis","display_name":"Matrix analysis","score":0.474250465631485},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4731769859790802},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46245574951171875},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44273650646209717},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.4171571731567383},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2012072205543518},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10572925209999084},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0741533637046814}],"concepts":[{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.8934028148651123},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8130024671554565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8029608726501465},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6653523445129395},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.5698402523994446},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5482174158096313},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5392808318138123},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.474250465631485},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4731769859790802},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46245574951171875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44273650646209717},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4171571731567383},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2012072205543518},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10572925209999084},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0741533637046814},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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":4,"locations":[{"id":"doi:10.1137/151006159","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151006159","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.697.2068","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.697.2068","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/%7Ebenzi/Web_papers/final_kron.pdf","raw_type":"text"},{"id":"pmh:oai:cris.unibo.it:11585/517563","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/517563","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ricerca.sns.it:11384/75248","is_oa":true,"landing_page_url":"http://hdl.handle.net/11384/75248","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ricerca.sns.it:11384/75248","is_oa":true,"landing_page_url":"http://hdl.handle.net/11384/75248","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W105839681","https://openalex.org/W216856155","https://openalex.org/W1483073639","https://openalex.org/W1515416301","https://openalex.org/W1527992869","https://openalex.org/W1530783572","https://openalex.org/W1547037458","https://openalex.org/W1580820409","https://openalex.org/W1922629554","https://openalex.org/W1964074933","https://openalex.org/W1966103153","https://openalex.org/W1966599983","https://openalex.org/W1970420250","https://openalex.org/W1975118022","https://openalex.org/W1977534155","https://openalex.org/W1982612743","https://openalex.org/W1984347942","https://openalex.org/W2014887218","https://openalex.org/W2016982898","https://openalex.org/W2021196318","https://openalex.org/W2027395754","https://openalex.org/W2029894628","https://openalex.org/W2032793159","https://openalex.org/W2034716359","https://openalex.org/W2038535655","https://openalex.org/W2040566538","https://openalex.org/W2049766166","https://openalex.org/W2060474950","https://openalex.org/W2063332531","https://openalex.org/W2065205300","https://openalex.org/W2072907984","https://openalex.org/W2078440628","https://openalex.org/W2088576025","https://openalex.org/W2088666624","https://openalex.org/W2102087421","https://openalex.org/W2104756076","https://openalex.org/W2107330716","https://openalex.org/W2128792640","https://openalex.org/W2198697385","https://openalex.org/W2572784842","https://openalex.org/W2950119333","https://openalex.org/W2963315512","https://openalex.org/W3102812969","https://openalex.org/W3121465581"],"related_works":["https://openalex.org/W2369793817","https://openalex.org/W2364489971","https://openalex.org/W2889760420","https://openalex.org/W1984341342","https://openalex.org/W2036077645","https://openalex.org/W2191009027","https://openalex.org/W269260623","https://openalex.org/W2795648316","https://openalex.org/W152487970","https://openalex.org/W1942047793"],"abstract_inverted_index":{"We":[0,69],"present":[1],"decay":[2,56],"bounds":[3,50],"for":[4],"completely":[5],"monotonic":[6],"functions":[7,35,62],"of":[8,21,58,61,63],"Hermitian":[9],"matrices,":[10],"where":[11],"the":[12,27,29,48,53,59],"matrix":[13],"argument":[14],"is":[15],"banded":[16,22],"or":[17],"a":[18],"Kronecker":[19,66],"sum":[20,67],"matrices.":[23,77],"This":[24],"class":[25],"includes":[26],"exponential,":[28],"negative":[30],"fractional":[31],"roots,":[32],"and":[33],"other":[34],"that":[36],"are":[37],"important":[38],"in":[39],"applications.":[40],"Besides":[41],"being":[42],"significantly":[43],"tighter":[44],"than":[45],"previous":[46],"estimates,":[47],"new":[49],"closely":[51],"capture":[52],"actual":[54],"(nonmonotonic)":[55],"behavior":[57],"entries":[60],"matrices":[64],"with":[65],"structure.":[68],"also":[70],"discuss":[71],"extensions":[72],"to":[73],"more":[74],"general":[75],"sparse":[76]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":9}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}