{"id":"https://openalex.org/W2051561721","doi":"https://doi.org/10.1137/s0036139901386375","title":"Fr\u00e9chet Derivatives for Some Bilinear Inverse Problems","display_name":"Fr\u00e9chet Derivatives for Some Bilinear Inverse Problems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2051561721","doi":"https://doi.org/10.1137/s0036139901386375","mag":"2051561721"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139901386375","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139901386375","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5032846501","display_name":"Frank Natterer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Frank Natterer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085689250","display_name":"Helmut Sielschott","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Helmut Sielschott","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021691282","display_name":"Oliver Dorn","orcid":"https://orcid.org/0000-0002-1529-7295"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oliver Dorn","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033688585","display_name":"Thomas Dierkes","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Dierkes","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078449262","display_name":"Victor Palamodov","orcid":"https://orcid.org/0000-0003-1667-5398"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Victor Palamodov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032846501"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3882,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.78361452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"62","issue":"6","first_page":"2092","last_page":"2113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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":0.9998999834060669,"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.998199999332428,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9959999918937683,"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/inverse-problem","display_name":"Inverse problem","score":0.7889976501464844},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6845497488975525},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5636345744132996},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5485202074050903},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5420762300491333},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5355797410011292},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5200569033622742},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4896460175514221},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4289097785949707},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14352521300315857},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1252996325492859}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.7889976501464844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6845497488975525},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5636345744132996},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5485202074050903},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5420762300491333},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5355797410011292},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5200569033622742},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4896460175514221},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4289097785949707},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14352521300315857},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1252996325492859},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139901386375","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139901386375","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W138212814","https://openalex.org/W627539672","https://openalex.org/W1506726083","https://openalex.org/W1583686354","https://openalex.org/W1597209545","https://openalex.org/W1972393088","https://openalex.org/W1972873815","https://openalex.org/W1973039295","https://openalex.org/W1976610132","https://openalex.org/W1980124656","https://openalex.org/W1996484806","https://openalex.org/W1996811888","https://openalex.org/W2033106066","https://openalex.org/W2036941264","https://openalex.org/W2038376073","https://openalex.org/W2049660658","https://openalex.org/W2082691870","https://openalex.org/W2090669915","https://openalex.org/W2092746511","https://openalex.org/W2095361687","https://openalex.org/W2100951241","https://openalex.org/W2163840973","https://openalex.org/W2167607665","https://openalex.org/W2317107851","https://openalex.org/W2567736332","https://openalex.org/W3021722416","https://openalex.org/W4212960264","https://openalex.org/W4285037076"],"related_works":["https://openalex.org/W2165589608","https://openalex.org/W3093557575","https://openalex.org/W2354231916","https://openalex.org/W2162140574","https://openalex.org/W3182767856","https://openalex.org/W2354073393","https://openalex.org/W2361009070","https://openalex.org/W2331917905","https://openalex.org/W3155039083","https://openalex.org/W1970914699"],"abstract_inverted_index":{"In":[0],"many":[1],"inverse":[2,43,112],"problems":[3,105],"a":[4,15,26],"functional":[5],"of":[6,19,41,49,57,62],"u":[7,13],"is":[8,25,64,91,100],"given":[9],"by":[10],"measurements,":[11],"where":[12],"solves":[14],"partial":[16],"differential":[17],"equation":[18,79,86],"the":[20,42,46,51,58,84,92,95],"type":[21],"L(p)u+Su=q.":[22],"Here":[23],"q":[24],"known":[27],"source":[28],"term,":[29],"and":[30,83],"L(p),":[31],"S":[32],"are":[33,107],"operators,":[34],"with":[35],"p":[36],"as":[37],"an":[38,77],"unknown":[39],"parameter":[40],"problem.":[44],"For":[45],"numerical":[47],"reconstruction":[48],"p,":[50],"heuristically":[52],"derived":[53],"Fr\u00e9chet":[54],"derivative":[55,93],"R'":[56,90],"mapping":[59],"$R:p\\rightarrow$":[60],"\"measurementfunctional":[61],"u\"":[63],"often":[65],"used.":[66],"We":[67],"show":[68],"for":[69,110],"three":[70],"problems---a":[71],"transport":[72],"problem":[73],"in":[74,87,94],"optical":[75],"tomography,":[76,82],"elliptic":[78],"governing":[80],"near-infrared":[81],"wave":[85],"moving":[88],"media---that":[89],"strict":[96],"sense.":[97],"Our":[98],"method":[99],"applicable":[101],"to":[102],"more":[103],"general":[104],"than":[106],"established":[108],"methods":[109],"similar":[111],"problems.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}