Set-Valued Interpolation

G. Perria: Set-Valued Interpolation
Bayreuther Mathematische Schriften 79, vi + 154 pp., in: Bayreuth, Germany, 2007

ISBN/ISSN/ISMV Nummer: 0172-1062
MR Nummer: 2791532
Zentralblattnummer: 1128.26018
Keywords: set-valued mapping; polynomial interpolation; directed derivative; divided difference; Kergin interpolation; directed sets; embedding of convex, compact sets; directed sets; embedding of convex, compact sets
Mathematics Subject Classification Code: 26E25 (49J53 41A10 58C06 47H04)


1. Overview
2. Theoretical Background
2.1 Preliminaries
2.2 The Directed Sets
2.3 The Bochner Integral
2.4 Metrics in the Space of Compact Convex Sets
3. Differentiation. Characterisation of Smooth Set-Valued Functions
3.1 The Directed Derivative
3.2 Characterisation of Smoothness
3.3 Classes of Directed-Differentiable Functions
3.4 A Non-Smooth Case
3.5 Lipschitz-Continuity
4. Divided Differences for Set-Valued Functions
4.1 Preliminaries
4.2 The Definition of the Divided Differences
4.3 The Hermite-Genocchi Formula
5. Set-Valued Polynomial Interpolation
5.1 Preliminaries
5.2 The Interpolating Map
5.3 Remainder Formulae and Error Estimates
5.4 Alternative Proof of Some Major Theorems
6. Numerical Applications
6.1 The Error of Approximation
6.2 Numerical Applications
7. A Short Description of the Implementation: SVUPI
7.1 Computation Schemes
7.2 Establishing the Software Components
7.3 The Programming Idioms. The Declaration of Some Major Classes

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