Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators
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A01=Alona Mokhov
A01=Elza Farkhi
A01=Nira Dyn
Approximation
Author_Alona Mokhov
Author_Elza Farkhi
Author_Nira Dyn
Category=PBPD
Category=PBW
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Hausdorff Metric
Metric Average
Metric Spaces
Minkowski Sum
Parameterization of Sets
Positive Operators
Set Operations
Set-Valued
Product details
- ISBN 9781783263028
- Publication Date: 18 Dec 2014
- Publisher: Imperial College Press
- Publication City/Country: GB
- Product Form: Hardback
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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.
