{"id":"https://openalex.org/W2008887064","doi":"https://doi.org/10.1137/s0895479899355025","title":"The Use and Properties of Tikhonov Filter Matrices","display_name":"The Use and Properties of Tikhonov Filter Matrices","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2008887064","doi":"https://doi.org/10.1137/s0895479899355025","mag":"2008887064"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479899355025","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899355025","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025647215","display_name":"M\u00e5rten Gulliksson","orcid":"https://orcid.org/0000-0003-0332-2315"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marten Gulliksson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053176705","display_name":"Per-\u00c5ke Wedin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Per-\u00c5ke Wedin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025647215"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1282,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.74356517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"1","first_page":"276","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9860000014305115,"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"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9860000014305115,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9749000072479248,"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/T13257","display_name":"Advanced Control and Stabilization in Aerospace Systems","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.9683508276939392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8047727346420288},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.5912978649139404},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5505964756011963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5197831988334656},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.49645406007766724},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4600927233695984},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.45781436562538147},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4386647343635559},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33839160203933716},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.21159875392913818},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18118196725845337},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.17713803052902222},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11575481295585632},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09043365716934204},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05472651124000549}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.9683508276939392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8047727346420288},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.5912978649139404},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5505964756011963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5197831988334656},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.49645406007766724},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4600927233695984},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.45781436562538147},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4386647343635559},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33839160203933716},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.21159875392913818},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18118196725845337},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.17713803052902222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11575481295585632},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09043365716934204},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05472651124000549},{"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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":1,"locations":[{"id":"doi:10.1137/s0895479899355025","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899355025","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2018089423","https://openalex.org/W2150200785","https://openalex.org/W4302564868"],"related_works":["https://openalex.org/W3103586881","https://openalex.org/W4313348341","https://openalex.org/W2950101867","https://openalex.org/W2521794430","https://openalex.org/W1531780090","https://openalex.org/W4301510292","https://openalex.org/W2510911034","https://openalex.org/W2373436489","https://openalex.org/W2005490094","https://openalex.org/W2016852860"],"abstract_inverted_index":{"We":[0,33],"consider":[1],"the":[2,20,40,55],"concept":[3],"of":[4,19],"Tikhonov":[5,21,41],"filter":[6,22,48],"matrices":[7,23,49],"in":[8],"connection":[9],"with":[10,27],"discrete":[11],"ill-posed":[12],"and":[13,30,60],"rank-deficient":[14],"linear":[15,43,56],"problems.":[16],"Important":[17],"properties":[18],"are":[24],"given":[25],"together":[26],"their":[28],"filtering":[29],"regularization":[31],"effects.":[32],"also":[34],"present":[35],"new":[36],"perturbation":[37,52],"identities":[38,53],"for":[39,54],"regularized":[42],"least":[44,57],"squares":[45,58],"problem":[46,59],"using":[47],"generalizing":[50],"well-known":[51],"pseudoinverses.":[61]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
