{"id":"https://openalex.org/W1496788307","doi":"https://doi.org/10.1007/978-3-642-04921-7_6","title":"Some Enhancements to Orthonormal Approximation of 2D Functions","display_name":"Some Enhancements to Orthonormal Approximation of 2D Functions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1496788307","doi":"https://doi.org/10.1007/978-3-642-04921-7_6","mag":"1496788307"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-04921-7_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-04921-7_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5010089327","display_name":"Bart\u0142omiej Beliczy\u0144ski","orcid":null},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Bartlomiej Beliczynski","raw_affiliation_strings":["Institute of Control and Industrial Electronics, Warsaw University of Technology, Warszawa, Poland","Warsaw University of Technology, Institute of Control and Industrial Electronics, Warszawa, Poland#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Control and Industrial Electronics, Warsaw University of Technology, Warszawa, Poland","institution_ids":["https://openalex.org/I108403487"]},{"raw_affiliation_string":"Warsaw University of Technology, Institute of Control and Industrial Electronics, Warszawa, Poland#TAB#","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010089327"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08299164,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"52","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.989300012588501,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.989300012588501,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/orthonormality","display_name":"Orthonormality","score":0.9558305740356445},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.9050589799880981},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6486606597900391},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6084938645362854},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5989015698432922},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5662454962730408},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5374150276184082},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5265493988990784},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5146921277046204},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.49852514266967773},{"id":"https://openalex.org/keywords/orthogonal-functions","display_name":"Orthogonal functions","score":0.49239933490753174},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4530567228794098},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.44903233647346497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4473768174648285},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4409734904766083},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4175407290458679},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4114260673522949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40619957447052},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24110999703407288},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19235441088676453},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08838808536529541}],"concepts":[{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.9558305740356445},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.9050589799880981},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6486606597900391},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6084938645362854},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5989015698432922},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5662454962730408},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5374150276184082},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5265493988990784},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5146921277046204},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.49852514266967773},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.49239933490753174},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4530567228794098},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.44903233647346497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4473768174648285},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4409734904766083},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4175407290458679},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4114260673522949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40619957447052},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24110999703407288},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19235441088676453},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08838808536529541},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-04921-7_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-04921-7_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1487100330","https://openalex.org/W1585230165","https://openalex.org/W1608130054","https://openalex.org/W2099759795","https://openalex.org/W2107221565","https://openalex.org/W2142544077","https://openalex.org/W2502391678","https://openalex.org/W3125537303"],"related_works":["https://openalex.org/W2078597522","https://openalex.org/W1496788307","https://openalex.org/W2004773025","https://openalex.org/W2064438860","https://openalex.org/W2072345404","https://openalex.org/W2095448080","https://openalex.org/W1547339931","https://openalex.org/W2027500037","https://openalex.org/W2564564625","https://openalex.org/W2166866359"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}