Algorithm 860: SimpleS—an extension of Freudenthal's simplex subdivision

Authors:
Eduardo N. Gonçalves;Reinaldo M. Palhares;Ricardo H. C. Takahashi;Renato C. Mesquita
Affiliations:
Federal Center of Technological Education of Minas Gerais, Belo Horizonte, MG, Brazil;Federal University of Minas Gerais, Belo Horizonte, MG, Brazil;Federal University of Minas Gerais, Belo Horizonte, MG, Brazil;Federal University of Minas Gerais, Belo Horizonte, MG, Brazil
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2006

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Abstract

This article presents a simple efficient algorithm for the subdivision of a d-dimensional simplex in kd simplices, where k 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 kd subdivision, and is considerably simpler than the RedRefinementND 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.