{"id":"https://openalex.org/W2598135565","doi":"https://doi.org/10.1007/s11075-017-0310-4","title":"Convergence properties of dynamic string-averaging projection methods in the presence of perturbations","display_name":"Convergence properties of dynamic string-averaging projection methods in the presence of perturbations","publication_year":2017,"publication_date":"2017-03-28","ids":{"openalex":"https://openalex.org/W2598135565","doi":"https://doi.org/10.1007/s11075-017-0310-4","mag":"2598135565"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-017-0310-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-017-0310-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-017-0310-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-017-0310-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072597621","display_name":"Christian Bargetz","orcid":"https://orcid.org/0000-0001-8525-0532"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]},{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT","IL"],"is_corresponding":true,"raw_author_name":"Christian Bargetz","raw_affiliation_strings":["Department of Mathematics, The Technion\u2014Israel Institute of Technology, 32000, Haifa, Israel","Department of Mathematics, University of Innsbruck, Technikerstra\u00dfe 13, 6020, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0001-8525-0532","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, 32000, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstra\u00dfe 13, 6020, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057413218","display_name":"Simeon Reich","orcid":"https://orcid.org/0000-0003-0780-1559"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Simeon Reich","raw_affiliation_strings":["Department of Mathematics, The Technion\u2014Israel Institute of Technology, 32000, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, 32000, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071059710","display_name":"Rafa\u0142 Zalas","orcid":"https://orcid.org/0000-0003-0193-9610"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Rafa\u0142 Zalas","raw_affiliation_strings":["Department of Mathematics, The Technion\u2014Israel Institute of Technology, 32000, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, 32000, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072597621"],"corresponding_institution_ids":["https://openalex.org/I174306211","https://openalex.org/I190249584"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.081,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.92344012,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"77","issue":"1","first_page":"185","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.996399998664856,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7980361580848694},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6892600655555725},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6591178774833679},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6072815656661987},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.603652834892273},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.4809917211532593},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4674428701400757},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.463421493768692},{"id":"https://openalex.org/keywords/normal-convergence","display_name":"Normal convergence","score":0.44734781980514526},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4205603301525116},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.22182443737983704},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21945348381996155},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15726357698440552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10149523615837097},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07035693526268005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7980361580848694},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6892600655555725},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6591178774833679},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6072815656661987},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.603652834892273},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.4809917211532593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4674428701400757},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.463421493768692},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.44734781980514526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4205603301525116},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.22182443737983704},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21945348381996155},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15726357698440552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10149523615837097},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07035693526268005},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11075-017-0310-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-017-0310-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-017-0310-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1703.07803","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.07803","pdf_url":"https://arxiv.org/pdf/1703.07803","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:diglib.uibk.ac.at/:4569316","is_oa":true,"landing_page_url":"https://resolver.obvsg.at/urn:nbn:at:at-ubi:3-7035","pdf_url":null,"source":{"id":"https://openalex.org/S4306401999","display_name":"Digital Library of the University of Innsbruck (University of Innsbruck)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I143397708","host_organization_name":"Innsbruck Medical University","host_organization_lineage":["https://openalex.org/I143397708"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s11075-017-0310-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-017-0310-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-017-0310-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2942734666","display_name":null,"funder_award_id":"389/12","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320326164","display_name":"Medizinische Universit\u00e4t Innsbruck","ror":"https://ror.org/03pt86f80"},{"id":"https://openalex.org/F4320327491","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2598135565.pdf","grobid_xml":"https://content.openalex.org/works/W2598135565.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W198508004","https://openalex.org/W205960364","https://openalex.org/W613392520","https://openalex.org/W1210354003","https://openalex.org/W1210424432","https://openalex.org/W1515429414","https://openalex.org/W1520261777","https://openalex.org/W1575441071","https://openalex.org/W1585386565","https://openalex.org/W1853237406","https://openalex.org/W1972150100","https://openalex.org/W1975552883","https://openalex.org/W1975567493","https://openalex.org/W1986280275","https://openalex.org/W1988262431","https://openalex.org/W1998428773","https://openalex.org/W2001032119","https://openalex.org/W2002110362","https://openalex.org/W2008965355","https://openalex.org/W2011347843","https://openalex.org/W2033511209","https://openalex.org/W2038085385","https://openalex.org/W2041871718","https://openalex.org/W2041880818","https://openalex.org/W2061024081","https://openalex.org/W2069491950","https://openalex.org/W2074214991","https://openalex.org/W2094508696","https://openalex.org/W2097629080","https://openalex.org/W2099454114","https://openalex.org/W2100885264","https://openalex.org/W2109982246","https://openalex.org/W2114331123","https://openalex.org/W2135528585","https://openalex.org/W2146418213","https://openalex.org/W2150227611","https://openalex.org/W2168734152","https://openalex.org/W2291131262","https://openalex.org/W2570616195","https://openalex.org/W2598996488","https://openalex.org/W2953267691","https://openalex.org/W2962704982","https://openalex.org/W2962956860","https://openalex.org/W2963341355","https://openalex.org/W3099167956","https://openalex.org/W3102828240","https://openalex.org/W3103639684","https://openalex.org/W4229650096","https://openalex.org/W4254884888","https://openalex.org/W4254978899","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2180233726","https://openalex.org/W2551580799","https://openalex.org/W2274896682","https://openalex.org/W4281774867","https://openalex.org/W2024085672","https://openalex.org/W2032940239","https://openalex.org/W4285029395","https://openalex.org/W2008596493","https://openalex.org/W4301012366","https://openalex.org/W2285605129"],"abstract_inverted_index":{"Assuming":[0],"that":[1,34],"the":[2,18,35,45,54,79],"absence":[3],"of":[4,20,23,27,38,47,58],"perturbations":[5],"guarantees":[6],"weak":[7],"or":[8],"strong":[9],"convergence":[10,36,56],"to":[11,53,78],"a":[12],"common":[13],"fixed":[14],"point,":[15],"we":[16,64,70],"study":[17],"behavior":[19],"perturbed":[21],"products":[22,40],"an":[24],"infinite":[25],"family":[26],"nonexpansive":[28],"operators.":[29],"Our":[30],"main":[31],"result":[32,74],"indicates":[33],"rate":[37,57],"unperturbed":[39],"is":[41],"essentially":[42],"preserved":[43],"in":[44,50],"presence":[46],"perturbations.":[48],"This,":[49],"particular,":[51],"applies":[52],"linear":[55],"dynamic":[59],"string-averaging":[60],"projection":[61],"methods,":[62],"which":[63],"establish":[65],"here":[66],"as":[67],"well.":[68],"Moreover,":[69],"show":[71],"how":[72],"this":[73],"can":[75],"be":[76],"applied":[77],"superiorization":[80],"methodology.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-04-07T00:00:00"}
