{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:38:31Z","timestamp":1750307911757,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2006,12,1]],"date-time":"2006-12-01T00:00:00Z","timestamp":1164931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:p>\n            This article presents a simple efficient algorithm for the subdivision of a\n            <jats:italic>d<\/jats:italic>\n            -dimensional simplex in\n            <jats:italic>k<\/jats:italic>\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            simplices, where\n            <jats:italic>k<\/jats:italic>\n            is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of\n            <jats:italic>k<\/jats:italic>\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            subdivision, and is considerably simpler than the\n            <jats:italic>RedRefinementND<\/jats:italic>\n            algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.\n          <\/jats:p>","DOI":"10.1145\/1186785.1186792","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"609-621","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Algorithm 860"],"prefix":"10.1145","volume":"32","author":[{"given":"Eduardo N.","family":"Gon\u00e7alves","sequence":"first","affiliation":[{"name":"Federal Center of Technological Education of Minas Gerais, Belo Horizonte, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reinaldo M.","family":"Palhares","sequence":"additional","affiliation":[{"name":"Federal University of Minas Gerais, Belo Horizonte, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo H. C.","family":"Takahashi","sequence":"additional","affiliation":[{"name":"Federal University of Minas Gerais, Belo Horizonte, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renato C.","family":"Mesquita","sequence":"additional","affiliation":[{"name":"Federal University of Minas Gerais, Belo Horizonte, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2006,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Balakrishnan V. Boyd S. and Balemi S. 1991. Computing the minimum stability degree of parameter-dependent linear systems. In Control of Uncertain Dynamic Systems S. P. Bhattacharyya and L. H. Keel Eds. CRC Press Boca Raton FL 359--378.  Balakrishnan V. Boyd S. and Balemi S. 1991. Computing the minimum stability degree of parameter-dependent linear systems. In Control of Uncertain Dynamic Systems S. P. Bhattacharyya and L. H. Keel Eds. CRC Press Boca Raton FL 359--378.","DOI":"10.1201\/9781003067702-28"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/235815.235821"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050475"},{"key":"e_1_2_2_4_1","volume-title":"Computational Geometry: Algorithms and Applications","author":"de Berg M.","year":"1998","unstructured":"de Berg , M. , Kreveld , M. V. , Overmas , M. , and Schwarzkopt , O . 1998 . Computational Geometry: Algorithms and Applications . Springer Verlag , Berlin . de Berg, M., Kreveld, M. V., Overmas, M., and Schwarzkopt, O. 1998. Computational Geometry: Algorithms and Applications. Springer Verlag, Berlin."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s4540010063"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/838250.838254"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cta:20045041"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(93)E0057-K"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1186785.1186792","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1186785.1186792","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:47:52Z","timestamp":1750258072000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1186785.1186792"}},"subtitle":["SimpleS\u2014an extension of Freudenthal's simplex subdivision"],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["10.1145\/1186785.1186792"],"URL":"https:\/\/doi.org\/10.1145\/1186785.1186792","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2006,12]]},"assertion":[{"value":"2006-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}