Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators Adaptation of Classical Approximation Operators By: Nira Dyn; Elza Farkhi; Alona Mokhov Publisher: ICP Print ISBN: 9781783263028, 1783263024 eText ISBN: 9781783263042, 1783263040 Pages: 168 Format: EPUB Available from $ 34.00 USD SKU: 9781783263042 This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values. Contents: Scientific Background: On Functions with Values in Metric Spaces On Sets On Set-Valued Functions (SVFs) Approximation of SVFs with Images in ℝn: Methods Based on Canonical Representations Methods Based on Minkowski Convex Combinations Methods Based on the Metric Average Methods Based on Metric Linear Combinations Methods Based on Metric Selections Approximation of SVFs with Images in ℝ: SVFs with Images in ℝ Multi-Segmental and Topological Representations Methods Based on Topological Representation Researchers and graduate students in the fields of approximation theory, set-valued analysis, dynamical systems, control and game theory, optimization and geometric modeling. SKU: 9781783263028 Ebooks here: https://ebookscoffee.sellpass.io/pr...aptation-Of-Classical-Approximation-Operators
