{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:53:37Z","timestamp":1759838017028},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","funder":[{"name":"Al-Zaytoonah University of Jordan","award":["2019-2018\/585\/G12"],"award-info":[{"award-number":["2019-2018\/585\/G12"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Info. Know. Mgmt."],"published-print":{"date-parts":[[2020,3]]},"abstract":"<jats:p> Polynomial functions [Formula: see text] of degree [Formula: see text] have a form in the Bernstein basis defined over [Formula: see text]-dimensional simplex [Formula: see text]. The Bernstein coefficients exhibit a number of special properties. The function [Formula: see text] can be optimised by the smallest and largest Bernstein coefficients (enclosure bounds) over [Formula: see text]. By a proper choice of barycentric subdivision steps of [Formula: see text], we prove the inclusion property of Bernstein enclosure bounds. To this end, we provide an algorithm that computes the Bernstein coefficients over subsimplices. These coefficients are collected in an [Formula: see text]-dimensional array in the field of computer-aided geometric design. Such a construct is typically classified as a patch. We show that the Bernstein coefficients of [Formula: see text] over the faces of a simplex coincide with the coefficients contained in the patch. <\/jats:p>","DOI":"10.1142\/s0219649220400018","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T07:30:54Z","timestamp":1583998254000},"page":"2040001","source":"Crossref","is-referenced-by-count":6,"title":["Fast Computation of Polynomial Data Points Over Simplicial Face Values"],"prefix":"10.1142","volume":"19","author":[{"given":"Tareq","family":"Hamadneh","sequence":"first","affiliation":[{"name":"Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, Jordan"}]},{"given":"Hassan","family":"Al-Zoubi","sequence":"additional","affiliation":[{"name":"Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, Jordan"}]},{"given":"Saleh Ali","family":"Alomari","sequence":"additional","affiliation":[{"name":"Faculty of Science and Information Technology, Jadara University, Irbid, Jordan"}]}],"member":"219","published-online":{"date-parts":[[2020,3,12]]},"reference":[{"key":"S0219649220400018BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/0505007"},{"key":"S0219649220400018BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.01.055"},{"key":"S0219649220400018BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(86)90016-6"},{"key":"S0219649220400018BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2012.03.001"},{"key":"S0219649220400018BIB006","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/978-3-319-31769-4_14","volume-title":"SCAN 2015: Scientific Computing, Computer Arithmetic, and Validated Numerics","volume":"9553","author":"Garloff J","year":"2015"},{"key":"S0219649220400018BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-003-1471-7"},{"key":"S0219649220400018BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6280-4_9"},{"key":"S0219649220400018BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/JEEIT.2019.8717503"},{"key":"S0219649220400018BIB012","doi-asserted-by":"publisher","DOI":"10.23919\/ACC.2018.8431599"},{"key":"S0219649220400018BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238236"},{"key":"S0219649220400018BIB016","first-page":"11","volume":"17","author":"Leroy R","year":"2012","journal-title":"Reliable Computing"},{"key":"S0219649220400018BIB017","series-title":"Encyclopedia of Mathematics and its Applications","volume-title":"Interval Methods for Systems of Equations","volume":"37","author":"Neumaier A","year":"1990"},{"key":"S0219649220400018BIB018","doi-asserted-by":"publisher","DOI":"10.1145\/198429.198434"},{"key":"S0219649220400018BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(00)00155-9"},{"key":"S0219649220400018BIB020","doi-asserted-by":"publisher","DOI":"10.1145\/2562059.2562132"},{"key":"S0219649220400018BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-18161-5_37"},{"key":"S0219649220400018BIB022","doi-asserted-by":"publisher","DOI":"10.1109\/9.661615"}],"container-title":["Journal of Information &amp; Knowledge Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219649220400018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,13]],"date-time":"2020-05-13T08:23:44Z","timestamp":1589358224000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219649220400018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3]]},"references-count":17,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["10.1142\/S0219649220400018"],"URL":"https:\/\/doi.org\/10.1142\/s0219649220400018","relation":{},"ISSN":["0219-6492","1793-6926"],"issn-type":[{"value":"0219-6492","type":"print"},{"value":"1793-6926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3]]}}}