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Title: Convergence Properties of Iterations Using Sets
Language: English
Authors: Rump, Siegfried M. 
Keywords: convergence;iteration;inclusion method
Issue Date: 1991
Source: Wissenschaftliche Zeitschrift, TU Leipzig, 15(6):427–432, 1991
Abstract (english): In the literature efficient algorithms have been described for calculating guaranteed inclusions for the solution of a number of standard numerical problems. The inclusions are given by means of a set containing the solution. In [11,12] this set is calculated using an affine iteration which stops after a nonempty and compact set has been mapped into itself. In this paper different types of auch sets are investigated, namely general sets, hyperrectangles and standard simlices. For affine iterations using those types of sets global convergence properties are given. Here, global convergence means that the iteration stops for every starting set with a set being mapped into itself.
DOI: 10.15480/882.297
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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