{"id":"https://openalex.org/W2963783420","doi":"https://doi.org/10.2478/cmam-2012-0026","title":"Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods","display_name":"Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2963783420","doi":"https://doi.org/10.2478/cmam-2012-0026","mag":"2963783420"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2012-0026","is_oa":false,"landing_page_url":"https://doi.org/10.2478/cmam-2012-0026","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in 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/A5088656822","display_name":"Johannes Kraus","orcid":"https://orcid.org/0000-0003-2261-599X"},"institutions":[{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Johannes Kraus","raw_affiliation_strings":["1Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Altenberger Str. 69, 4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Altenberger Str. 69, 4040 Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panayot Vassilevski","raw_affiliation_strings":["2Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, U.S.A","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074536850","display_name":"Ludmil Zikatanov","orcid":"https://orcid.org/0000-0002-5189-4230"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ludmil Zikatanov","raw_affiliation_strings":["3Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"3Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088656822"],"corresponding_institution_ids":["https://openalex.org/I4210158379"],"apc_list":null,"apc_paid":null,"fwci":3.148,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91682031,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"4","first_page":"448","last_page":"468"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8072470426559448},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5815581679344177},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5688803791999817},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.547825038433075},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5371940732002258},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49767282605171204},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.49355947971343994},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.48587268590927124},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.47642025351524353},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.43991559743881226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41441091895103455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1944558024406433},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11609312891960144}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8072470426559448},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5815581679344177},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5688803791999817},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.547825038433075},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5371940732002258},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49767282605171204},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.49355947971343994},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.48587268590927124},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.47642025351524353},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.43991559743881226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41441091895103455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1944558024406433},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11609312891960144},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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:10.2478/cmam-2012-0026","is_oa":false,"landing_page_url":"https://doi.org/10.2478/cmam-2012-0026","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2376029318","https://openalex.org/W2388301251","https://openalex.org/W3013941779","https://openalex.org/W1998659141","https://openalex.org/W3195376785","https://openalex.org/W2370435933","https://openalex.org/W138938013","https://openalex.org/W2947625790","https://openalex.org/W1975877275","https://openalex.org/W9397806"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"derive":[2],"defect":[3],"correction":[4],"scheme":[5],"for":[6,35],"constructing":[7],"the":[8,16,43,46,50,75,84,88,97],"sequence":[9],"of":[10,12,53,62,74,87],"polynomials":[11],"best":[13,54],"approximation":[14],"in":[15],"uniform":[17,93],"norm":[18],"to":[19,96],"1/x":[20],"on":[21,45,57],"a":[22,58,71,81],"finite":[23],"interval":[24],"with":[25,70,94],"positive":[26],"endpoints.":[27],"As":[28],"an":[29],"application,":[30],"we":[31,67,78],"consider":[32],"two-level":[33,90],"methods":[34],"scalar":[36],"elliptic":[37],"partial":[38],"differential":[39],"equation":[40],"(PDE),":[41],"where":[42],"relaxation":[44],"fine":[47],"grid":[48],"uses":[49],"aforementioned":[51],"polynomial":[52,64],"approximation.":[55],"Based":[56],"new":[59],"smoothing":[60],"property":[61],"this":[63],"smoother":[65],"that":[66,83],"prove,":[68],"combined":[69],"proper":[72],"choice":[73],"coarse":[76],"space,":[77],"obtain":[79],"as":[80],"corollary,":[82],"convergence":[85],"rate":[86],"resulting":[89],"method":[91],"is":[92],"respect":[95],"mesh":[98],"parameters,":[99],"coarsening":[100],"ratio":[101],"and":[102],"PDE":[103],"coefficient":[104],"variation.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2019-07-30T00:00:00"}