{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:30Z","timestamp":1760143590454,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071444","202103021223191","202303021221116","20231944"],"award-info":[{"award-number":["12071444","202103021223191","202303021221116","20231944"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Program of Shanxi Province","award":["12071444","202103021223191","202303021221116","20231944"],"award-info":[{"award-number":["12071444","202103021223191","202303021221116","20231944"]}]},{"name":"19th Graduate Science and Technology Project of North University of China","award":["12071444","202103021223191","202303021221116","20231944"],"award-info":[{"award-number":["12071444","202103021223191","202303021221116","20231944"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In Chuanming Zong\u2019s program to attack Hadwiger\u2019s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. and Yu et al. provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong\u2019s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.<\/jats:p>","DOI":"10.3390\/axioms13020132","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T10:40:15Z","timestamp":1708339215000},"page":"132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An Algorithm Based on Compute Unified Device Architecture for Estimating Covering Functionals of Convex Bodies"],"prefix":"10.3390","volume":"13","author":[{"given":"Xiangyang","family":"Han","sequence":"first","affiliation":[{"name":"School of Mathematics, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2499-2836","authenticated-orcid":false,"given":"Senlin","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longzhen","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Boltyanski, V., Martini, H., and Soltan, P.S. 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