{"id":"https://openalex.org/W2055128664","doi":"https://doi.org/10.1007/s11075-008-9244-1","title":"Error estimates for large-scale ill-posed problems","display_name":"Error estimates for large-scale ill-posed problems","publication_year":2008,"publication_date":"2008-10-22","ids":{"openalex":"https://openalex.org/W2055128664","doi":"https://doi.org/10.1007/s11075-008-9244-1","mag":"2055128664"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-008-9244-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-008-9244-1","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5072817181","display_name":"Lothar Reichel","orcid":"https://orcid.org/0000-0003-1729-6816"},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L. Reichel","raw_affiliation_strings":["Department of Mathematical Sciences, Kent State University, Kent, 9244, OH, USA","Kent State Univ"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Kent State University, Kent, 9244, OH, USA","institution_ids":["https://openalex.org/I149910238"]},{"raw_affiliation_string":"Kent State Univ","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068794378","display_name":"G. Rodr\u00edguez","orcid":"https://orcid.org/0000-0001-9054-8712"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Rodriguez","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e0 di Cagliari, Viale Merello 92, 09123, Cagliari, Italy","Universita\u0300 di Cagliari,"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e0 di Cagliari, Viale Merello 92, 09123, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]},{"raw_affiliation_string":"Universita\u0300 di Cagliari,","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027908804","display_name":"S. Seatzu","orcid":null},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"S. Seatzu","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e0 di Cagliari, Viale Merello 92, 09123, Cagliari, Italy","Universita\u0300 di Cagliari,"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e0 di Cagliari, Viale Merello 92, 09123, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]},{"raw_affiliation_string":"Universita\u0300 di Cagliari,","institution_ids":["https://openalex.org/I172446870"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072817181"],"corresponding_institution_ids":["https://openalex.org/I149910238"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.43,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.59796087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"3","first_page":"341","last_page":"361"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9947999715805054,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.9122663736343384},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.7405686974525452},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6999680995941162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6598958969116211},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.6015087366104126},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.5919358730316162},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5874797701835632},{"id":"https://openalex.org/keywords/backus\u2013gilbert-method","display_name":"Backus\u2013Gilbert method","score":0.5707865357398987},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5211784243583679},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.4956437349319458},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.43573176860809326},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3547526001930237},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2746754288673401},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23065686225891113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16330868005752563},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08202061057090759}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.9122663736343384},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.7405686974525452},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6999680995941162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6598958969116211},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.6015087366104126},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.5919358730316162},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5874797701835632},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.5707865357398987},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5211784243583679},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.4956437349319458},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.43573176860809326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3547526001930237},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2746754288673401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23065686225891113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16330868005752563},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08202061057090759},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11075-008-9244-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-008-9244-1","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.2565","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.2565","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.kent.edu/~reichel/publications/errest.pdf","raw_type":"text"},{"id":"pmh:oai:iris.unica.it:11584/15549","is_oa":false,"landing_page_url":"http://hdl.handle.net/11584/15549","pdf_url":null,"source":{"id":"https://openalex.org/S4377196293","display_name":"UNICA IRIS Institutional Research Information System (University of Cagliari)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172446870","host_organization_name":"University of Cagliari","host_organization_lineage":["https://openalex.org/I172446870"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W48622852","https://openalex.org/W64572908","https://openalex.org/W112019301","https://openalex.org/W1570089119","https://openalex.org/W1570537360","https://openalex.org/W1593505867","https://openalex.org/W1594234351","https://openalex.org/W1975753100","https://openalex.org/W1978528548","https://openalex.org/W1981076909","https://openalex.org/W1984903808","https://openalex.org/W1998762105","https://openalex.org/W1999801902","https://openalex.org/W2003264844","https://openalex.org/W2005140191","https://openalex.org/W2012841869","https://openalex.org/W2015204290","https://openalex.org/W2017387343","https://openalex.org/W2038273756","https://openalex.org/W2059693947","https://openalex.org/W2089349959","https://openalex.org/W2097897435","https://openalex.org/W2113834512","https://openalex.org/W2145962863","https://openalex.org/W2168913925","https://openalex.org/W2186391130"],"related_works":["https://openalex.org/W1947575127","https://openalex.org/W2374214022","https://openalex.org/W1612082733","https://openalex.org/W2510911034","https://openalex.org/W4385317013","https://openalex.org/W2118558328","https://openalex.org/W2061466028","https://openalex.org/W2353861642","https://openalex.org/W2521794430","https://openalex.org/W2054008566"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}