Variational Theory of Splines

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

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.—?-Approximations and Data Compression.- 12. Algorithms for Optimal Smoothing Parameter.- Appendices.- Theorems from Functional Analysis Used in This Book.- A.1 Convergence in Hilbert Space.- A.2 Theorems on Linear Operators.- A.3 Sobolev Spaces in Domain.- On Software Investigations in Splines.- B.1 One-Dimensional Case.- B.2 Multi-Dimensional Case.