Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators
Approximation Of Set-valued Functions: Adaptation Of Classical Approximation Operators

Author: Nira Dyn

Publisher: World Scientific

Published: 2014-10-30

Total Pages: 168

ISBN-13: 1783263040

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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.

Approximation of Vector Valued Functions
Approximation of Vector Valued Functions

Author:

Publisher: Elsevier

Published: 2011-10-10

Total Pages: 235

ISBN-13: 0080871364

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This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained. The amount of Functional Analysis required is minimal, except for Chapter 8. The book can be used by graduate students who have taken the usual first-year real and complex analysis courses.

Approximation of Set-valued Functions
Approximation of Set-valued Functions

Author: Nira Dyn

Publisher:

Published: 2014

Total Pages: 153

ISBN-13: 9781783263028

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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.

A Course in Functional Analysis and Measure Theory
A Course in Functional Analysis and Measure Theory

Author: Vladimir Kadets

Publisher: Springer

Published: 2018-07-10

Total Pages: 553

ISBN-13: 3319920049

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Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.

Trends in Approximation Theory
Trends in Approximation Theory

Author: Kirill Kopotun

Publisher:

Published: 2001

Total Pages: 456

ISBN-13:

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Contains a carefully edited selection of papers that were presented at the Symposium on Trends in Approximation Theory, held in May 2000, and at the Oslo Conference on Mathematical Methods for Curves and Surfaces, held in July 2000. Mathematical Methods for Curves and Surfaces covers topics from abstract approximation to wavelets.

An Introduction to Scientific, Symbolic, and Graphical Computation
An Introduction to Scientific, Symbolic, and Graphical Computation

Author: Eugene Fiume

Publisher: CRC Press

Published: 2018-10-08

Total Pages: 322

ISBN-13: 1439864462

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This down-to-earth introduction to computation makes use of the broad array of techniques available in the modern computing environment. A self-contained guide for engineers and other users of computational methods, it has been successfully adopted as a text in teaching the next generation of mathematicians and computer graphics majors.