{"id":"https://openalex.org/W4389784100","doi":"https://doi.org/10.3390/sym15122202","title":"A Simple Method for Constructing Symmetric Subdivision Schemes with High-Degree Polynomial Reproduction","display_name":"A Simple Method for Constructing Symmetric Subdivision Schemes with High-Degree Polynomial Reproduction","publication_year":2023,"publication_date":"2023-12-15","ids":{"openalex":"https://openalex.org/W4389784100","doi":"https://doi.org/10.3390/sym15122202"},"language":"en","primary_location":{"id":"doi:10.3390/sym15122202","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15122202","pdf_url":"https://www.mdpi.com/2073-8994/15/12/2202/pdf?version=1702628868","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/12/2202/pdf?version=1702628868","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106406907","display_name":"Jun Shi","orcid":"https://orcid.org/0000-0002-5572-0350"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Shi","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology, Hefei 230601, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei 230601, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045011804","display_name":"Jieqing Tan","orcid":"https://orcid.org/0000-0002-9275-0399"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jieqing Tan","raw_affiliation_strings":["School of Computer and Information, Hefei University of Technology, Hefei 230601, China","School of Mathematics, Hefei University of Technology, Hefei 230601, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Information, Hefei University of Technology, Hefei 230601, China","institution_ids":["https://openalex.org/I16365422"]},{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei 230601, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100425666","display_name":"Li Zhang","orcid":"https://orcid.org/0000-0002-9208-1949"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Zhang","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology, Hefei 230601, China"],"raw_orcid":"https://orcid.org/0000-0002-9208-1949","affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei 230601, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045011804"],"corresponding_institution_ids":["https://openalex.org/I16365422"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3246,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48330824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"15","issue":"12","first_page":"2202","last_page":"2202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"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/T10188","display_name":"Advanced machining processes and optimization","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T11138","display_name":"Tribology and Lubrication Engineering","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/subdivision","display_name":"Subdivision","score":0.9658963680267334},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7165340781211853},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6283581852912903},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6105382442474365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.547099232673645},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4299495816230774},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33937227725982666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33121249079704285},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3216283321380615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15453141927719116},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.050262659788131714}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.9658963680267334},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7165340781211853},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6283581852912903},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6105382442474365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.547099232673645},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4299495816230774},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33937227725982666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33121249079704285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3216283321380615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15453141927719116},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.050262659788131714},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15122202","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15122202","pdf_url":"https://www.mdpi.com/2073-8994/15/12/2202/pdf?version=1702628868","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5d411022649747f3b91cd74c26d568c8","is_oa":false,"landing_page_url":"https://doaj.org/article/5d411022649747f3b91cd74c26d568c8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 12, p 2202 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15122202","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15122202","pdf_url":"https://www.mdpi.com/2073-8994/15/12/2202/pdf?version=1702628868","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4967005443","display_name":null,"funder_award_id":"12001151","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G593046995","display_name":null,"funder_award_id":"62172135","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389784100.pdf","grobid_xml":"https://content.openalex.org/works/W4389784100.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1668107054","https://openalex.org/W1989601171","https://openalex.org/W2001867197","https://openalex.org/W2003173111","https://openalex.org/W2026381294","https://openalex.org/W2031327445","https://openalex.org/W2042273967","https://openalex.org/W2060903027","https://openalex.org/W2070725987","https://openalex.org/W2075492994","https://openalex.org/W2108871697","https://openalex.org/W2111669970","https://openalex.org/W2140359370","https://openalex.org/W2588222742","https://openalex.org/W2792254744","https://openalex.org/W2964107419","https://openalex.org/W2995470012"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2163269603","https://openalex.org/W2140072033","https://openalex.org/W4205312897","https://openalex.org/W1106115901","https://openalex.org/W2160084131"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"an":[5],"efficient":[6],"method":[7],"for":[8],"constructing":[9],"symmetric":[10,24],"subdivision":[11,25],"schemes":[12],"reproducing":[13],"high-degree":[14],"polynomials,":[15],"without":[16],"solving":[17],"a":[18],"system":[19],"of":[20,37,44,54],"linear":[21],"equations.":[22],"Original":[23],"and":[26],"its":[27],"deduced":[28],"subdivisions":[29],"have":[30],"similar":[31],"increasing":[32],"characteristics":[33],"to":[34,50],"the":[35,40,52,55],"family":[36],"pseudo-splines":[38],"from":[39],"polynomial":[41],"reproduction":[42],"point":[43],"view.":[45],"Several":[46],"examples":[47],"are":[48],"given":[49],"illustrate":[51],"efficiency":[53],"method.":[56]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
