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Convergence Properties of Iterations Using Sets
Citation Link: https://doi.org/10.15480/882.297
Publikationstyp
Journal Article
Date Issued
1991
Sprache
English
Author(s)
Institut
TORE-DOI
Citation
Wissenschaftliche Zeitschrift, TU Leipzig, 15(6):427–432, 1991
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.
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.
Subjects
convergence
iteration
inclusion method
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