Variational Theory of Splines / Edition 1

by Anatoly Yu. Bezhaev, Vladimir A. Vasilenko

Overview

This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.

Product Details

ISBN-13:	9781441933683
Publisher:	Springer US
Publication date:	12/01/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2001
Pages:	280
Product dimensions:	7.01(w) x 10.00(h) x 0.28(d)

Table of Contents

Preface. Introduction: A Guide to the Reader. 1. Splines in Hilbert Spaces. 2. Reproducing Mappings and Characterization of Splines. 3. General Convergence Techniques and Error Estimates for Interpolating Splines. 4. Splines in Subspaces. 5. Interpolating DM-Splines. 6. Splines on Manifolds. 7. Vector Splines. 8. Tensor and Blending Splines. 9. Optimal Approximation of Linear Operators. 10. Classification of Spline Objects. 11. SigmaPi-Approximations and Data Compression. 12. Algorithms for Optimal Smoothing Parameter. Appendices. Bibliography. Index.