{"id":"https://openalex.org/W1993774250","doi":"https://doi.org/10.1007/s00211-014-0629-x","title":"An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints","display_name":"An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints","publication_year":2014,"publication_date":"2014-04-17","ids":{"openalex":"https://openalex.org/W1993774250","doi":"https://doi.org/10.1007/s00211-014-0629-x","mag":"1993774250"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-014-0629-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-014-0629-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5026803226","display_name":"Maarten V. de Hoop","orcid":"https://orcid.org/0000-0002-6333-0379"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maarten V. de Hoop","raw_affiliation_strings":["Center for Computational and Applied Mathemematics, Purdue University, West Lafayette, IN, 47907, USA","Center for Computational and Applied Mathemematics, Purdue University, West Lafayette, USA 47907#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational and Applied Mathemematics, Purdue University, West Lafayette, IN, 47907, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Center for Computational and Applied Mathemematics, Purdue University, West Lafayette, USA 47907#TAB#","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059814255","display_name":"Lingyun Qiu","orcid":"https://orcid.org/0000-0002-2204-7235"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lingyun Qiu","raw_affiliation_strings":["Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, 55455, USA","Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, USA 55455#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, USA 55455#TAB#","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036501294","display_name":"Otmar Scherzer","orcid":"https://orcid.org/0000-0001-9378-7452"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Otmar Scherzer","raw_affiliation_strings":["Computational Science Center, University of Vienna, Nordbergstr. 15, 1090 , Vienna, Austria","Computational Science Center, University of Vienna, Nordbergstr. 15, 1090\u00a0, Vienna, Austria","Computational Science Center, University of Vienna, Vienna, Austria 1090#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Science Center, University of Vienna, Nordbergstr. 15, 1090 , Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Computational Science Center, University of Vienna, Nordbergstr. 15, 1090\u00a0, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Computational Science Center, University of Vienna, Vienna, Austria 1090#TAB#","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059814255"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":5.3772,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.95893639,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"129","issue":"1","first_page":"127","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9958000183105469,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.991100013256073,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8798390626907349},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7131404280662537},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6239973306655884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5558385848999023},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5440269708633423},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5371765494346619},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.528510570526123},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5012052059173584},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.47016140818595886},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.44124269485473633},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4409410357475281},{"id":"https://openalex.org/keywords/method-of-steepest-descent","display_name":"Method of steepest descent","score":0.4179420471191406},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3563418984413147},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31290000677108765},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07523393630981445}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8798390626907349},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7131404280662537},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6239973306655884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5558385848999023},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5440269708633423},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5371765494346619},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.528510570526123},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5012052059173584},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.47016140818595886},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.44124269485473633},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4409410357475281},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.4179420471191406},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3563418984413147},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31290000677108765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07523393630981445},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-014-0629-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-014-0629-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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":28,"referenced_works":["https://openalex.org/W614467277","https://openalex.org/W632810616","https://openalex.org/W1564864701","https://openalex.org/W1580825192","https://openalex.org/W1922505179","https://openalex.org/W1935121520","https://openalex.org/W1972581758","https://openalex.org/W1985999777","https://openalex.org/W1988978892","https://openalex.org/W1989436614","https://openalex.org/W2003165801","https://openalex.org/W2009666499","https://openalex.org/W2020408390","https://openalex.org/W2024375867","https://openalex.org/W2033468335","https://openalex.org/W2038010370","https://openalex.org/W2039466093","https://openalex.org/W2052797733","https://openalex.org/W2083244588","https://openalex.org/W2095463076","https://openalex.org/W2113740359","https://openalex.org/W2114161831","https://openalex.org/W2122148818","https://openalex.org/W2140414732","https://openalex.org/W2145753455","https://openalex.org/W3102176395","https://openalex.org/W3103184409","https://openalex.org/W4245503300"],"related_works":["https://openalex.org/W2367641551","https://openalex.org/W2010057865","https://openalex.org/W3040162855","https://openalex.org/W2481151534","https://openalex.org/W2363028408","https://openalex.org/W3212473031","https://openalex.org/W2392736212","https://openalex.org/W2352451880","https://openalex.org/W4287747751","https://openalex.org/W2063036314"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}