{"id":"https://openalex.org/W2083862580","doi":"https://doi.org/10.1109/tit.1981.1056378","title":"Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences","display_name":"Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences","publication_year":1981,"publication_date":"1981-07-01","ids":{"openalex":"https://openalex.org/W2083862580","doi":"https://doi.org/10.1109/tit.1981.1056378","mag":"2083862580"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1981.1056378","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1981.1056378","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5035921496","display_name":"P. Dewilde","orcid":"https://orcid.org/0000-0002-9553-1845"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"P. Dewilde","raw_affiliation_strings":["Department of Electrical Engineering, Delft University of Technnology, Delft, Netherlands","[Department of Electrical Engineering, Delft University of Technnology, Delft, Netherlands]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Delft University of Technnology, Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"[Department of Electrical Engineering, Delft University of Technnology, Delft, Netherlands]","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029694834","display_name":"Harry Dym","orcid":"https://orcid.org/0000-0003-0886-6266"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"H. Dym","raw_affiliation_strings":["Department of Theoretical Mathematics, Weizmann Institute of Science, Rehovot, Israel","[Department of Theoretical Mathematics, Weizmann Institute of Science, Rehovot, Israel]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Mathematics, Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"[Department of Theoretical Mathematics, Weizmann Institute of Science, Rehovot, Israel]","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.545,"has_fulltext":false,"cited_by_count":139,"citation_normalized_percentile":{"value":0.98251402,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"27","issue":"4","first_page":"446","last_page":"461"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9994999766349792,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9994999766349792,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9980000257492065,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5739517211914062},{"id":"https://openalex.org/keywords/lossless-compression","display_name":"Lossless compression","score":0.5344682335853577},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5187551975250244},{"id":"https://openalex.org/keywords/golomb-coding","display_name":"Golomb coding","score":0.4755235016345978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47293758392333984},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.4542461335659027},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44676411151885986},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44243136048316956},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40483736991882324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35094648599624634},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3356223404407501},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2768113613128662},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1250992715358734},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11641019582748413},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.09010720252990723}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5739517211914062},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.5344682335853577},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5187551975250244},{"id":"https://openalex.org/C66656319","wikidata":"https://www.wikidata.org/wiki/Q2638","display_name":"Golomb coding","level":5,"score":0.4755235016345978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47293758392333984},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.4542461335659027},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44676411151885986},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44243136048316956},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40483736991882324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35094648599624634},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3356223404407501},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2768113613128662},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1250992715358734},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11641019582748413},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.09010720252990723},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.0},{"id":"https://openalex.org/C13481523","wikidata":"https://www.wikidata.org/wiki/Q412438","display_name":"Image compression","level":4,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1981.1056378","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1981.1056378","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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":23,"referenced_works":["https://openalex.org/W330372241","https://openalex.org/W1576783654","https://openalex.org/W1604745759","https://openalex.org/W1908291764","https://openalex.org/W1964919148","https://openalex.org/W1982691093","https://openalex.org/W1993256723","https://openalex.org/W2000939927","https://openalex.org/W2005049658","https://openalex.org/W2018279569","https://openalex.org/W2031887434","https://openalex.org/W2060772540","https://openalex.org/W2164323769","https://openalex.org/W2312497442","https://openalex.org/W2326591006","https://openalex.org/W2524007148","https://openalex.org/W2997585286","https://openalex.org/W4238354054","https://openalex.org/W4246360657","https://openalex.org/W4250038851","https://openalex.org/W4388534025","https://openalex.org/W6727671524","https://openalex.org/W6772207760"],"related_works":["https://openalex.org/W2074882998","https://openalex.org/W1487470981","https://openalex.org/W784062432","https://openalex.org/W2030719776","https://openalex.org/W2155161695","https://openalex.org/W2187703884","https://openalex.org/W160243722","https://openalex.org/W1967661305","https://openalex.org/W1810995209","https://openalex.org/W2128890367"],"abstract_inverted_index":{"An":[0,60],"exact":[1,38],"and":[2,8,33,44,90,103,132],"approximate":[3,69],"realization":[4,39,74],"theory":[5,117],"for":[6,36,129],"estimation":[7,42],"model":[9,46],"filters":[10],"of":[11,20,40,51,62,86,111,114,118],"second-order":[12],"stationary":[13],"stochastic":[14],"sequences":[15],"is":[16,121,143],"presented.":[17],"The":[18,83,145],"properties":[19,85],"<tex":[21,53,70],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[22,54,71],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">J</tex>":[23,55,72],"-lossless":[24,56,73],"matrices":[25],"as":[26,48],"a":[27,45,49,52,109,124,152],"unifying":[28],"framework":[29],"are":[30,58,93,101,135],"used.":[31],"Necessary":[32],"sufficient":[34],"conditions":[35],"the":[37,63,81,98,105,115,140],"an":[41,68],"filter":[43,47],"submatrix":[50],"system":[57],"deduced.":[59],"extension":[61],"so-called":[64],"Schur":[65],"algorithm":[66],"yields":[67],"based":[75],"on":[76],"partial":[77,88,119],"past":[78],"information":[79],"about":[80],"process.":[82],"geometric":[84],"such":[87],"realizations":[89,120],"their":[91],"convergence":[92],"studied.":[94],"Finally,":[95],"connections":[96],"with":[97],"Nevanlinna-Pick":[99],"problem":[100],"made,":[102],"how":[104],"techniques":[106],"presented":[107],"constitute":[108],"generalization":[110],"many":[112],"aspects":[113],"Levinson-Szeg\u00f6":[116],"shown.":[122],"As":[123],"consequence":[125],"generalized":[126],"recursive":[127],"formulas":[128,134],"reproducing":[130],"kernels":[131],"Christoffel-Darboux":[133],"obtained.":[136],"In":[137],"this":[138],"paper":[139],"scalar":[141],"case":[142,147],"considered.":[144],"matrix":[146],"will":[148],"be":[149],"considered":[150],"in":[151],"separate":[153],"publication.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}