{"id":"https://openalex.org/W2317947248","doi":"https://doi.org/10.1112/s1461157012001167","title":"Examples of linear multi-box splines","display_name":"Examples of linear multi-box splines","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2317947248","doi":"https://doi.org/10.1112/s1461157012001167","mag":"2317947248"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157012001167","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157012001167","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5F3D1E9CC997947EE0FDAA20C9A705D1/S1461157012001167a.pdf/div-class-title-examples-of-linear-multi-box-splines-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5F3D1E9CC997947EE0FDAA20C9A705D1/S1461157012001167a.pdf/div-class-title-examples-of-linear-multi-box-splines-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000594295","display_name":"Abdellatif Bettayeb","orcid":null},"institutions":[{"id":"https://openalex.org/I82401606","display_name":"Jubail Industrial College","ror":"https://ror.org/01rw40d12","country_code":"SA","type":"education","lineage":["https://openalex.org/I82401606"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Abdellatif Bettayeb","raw_affiliation_strings":["General Studies Department, Jubail Industrial College, PO Box 10099 Jubail industrial city 31961, Saudi Arabia","General Studies Department, Jubail Industrial College, PO Box 10099 Jubail industrial city 31961, Saudi Arabia ("],"affiliations":[{"raw_affiliation_string":"General Studies Department, Jubail Industrial College, PO Box 10099 Jubail industrial city 31961, Saudi Arabia","institution_ids":["https://openalex.org/I82401606"]},{"raw_affiliation_string":"General Studies Department, Jubail Industrial College, PO Box 10099 Jubail industrial city 31961, Saudi Arabia (","institution_ids":["https://openalex.org/I82401606"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000594295"],"corresponding_institution_ids":["https://openalex.org/I82401606"],"apc_list":null,"apc_paid":null,"fwci":0.35031484,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6553794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":null,"first_page":"444","last_page":"462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8927013874053955},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.7315986156463623},{"id":"https://openalex.org/keywords/box-spline","display_name":"Box spline","score":0.7163816094398499},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.6025136709213257},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4591064453125},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4417873024940491},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4289952516555786},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.4259083569049835},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36342114210128784},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3008316159248352},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.11517268419265747}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8927013874053955},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.7315986156463623},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.7163816094398499},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.6025136709213257},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4591064453125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4417873024940491},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4289952516555786},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.4259083569049835},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36342114210128784},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3008316159248352},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.11517268419265747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157012001167","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157012001167","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5F3D1E9CC997947EE0FDAA20C9A705D1/S1461157012001167a.pdf/div-class-title-examples-of-linear-multi-box-splines-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1112/s1461157012001167","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157012001167","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5F3D1E9CC997947EE0FDAA20C9A705D1/S1461157012001167a.pdf/div-class-title-examples-of-linear-multi-box-splines-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2317947248.pdf","grobid_xml":"https://content.openalex.org/works/W2317947248.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W624439943","https://openalex.org/W1561837382","https://openalex.org/W2045005961","https://openalex.org/W2092399753","https://openalex.org/W4246088670"],"related_works":["https://openalex.org/W1992724775","https://openalex.org/W2380529683","https://openalex.org/W2165066371","https://openalex.org/W2133947431","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2130355919","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W1029391197"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"S":[2,5,66,77],"1":[3,6,59,67,78],"=":[4],"(":[7],"v":[8,11,37,40],"0":[9,22,38],",\u2026,":[10,39],"r":[12,41,61],"+1":[13,42],")":[14,62],"be":[15],"the":[16,49,52],"space":[17],"of":[18,30,51,63,65,76,84,86],"compactly":[19],"supported":[20],"C":[21],"piecewise":[23],"linear":[24,82],"functions":[25],"on":[26,48],"a":[27,70,80],"mesh":[28],"M":[29],"lines":[31],"through":[32],"\u2124":[33],"2":[34],"in":[35],"directions":[36],",":[43],"possibly":[44],"satisfying":[45],"some":[46,93],"restrictions":[47],"jumps":[50],"first":[53],"order":[54],"derivative.":[55],"A":[56],"sequence":[57],"\u03d5=(\u03d5":[58],",\u2026,\u03d5":[60],"elements":[64],"is":[68,79,105,112],"called":[69],"multi-box":[71,96,110],"spline":[72,111],"if":[73],"every":[74],"element":[75],"finite":[81],"combination":[83],"shifts":[85],"(the":[87],"components":[88],"of)":[89],"\u03d5.":[90],"We":[91],"give":[92],"examples":[94],"for":[95],"splines":[97],"and":[98],"show":[99],"that":[100,108],"they":[101],"are":[102],"stable.":[103],"It":[104],"further":[106],"shown":[107],"any":[109],"not":[113],"always":[114],"symmetric":[115]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
