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基本説明
This book is a systematic description of the variational theory of splines in Hilbert spaces.
Full Description
Th e vari a t i on al s p li ne t heo ry w h ic h orig i na t es from th e w ell-kn own p ap er b y J. e . Hollid a y ( 1957) i s t od a y a we ll- deve lo pe d fi eld in a p pr o x - mat i o n t he o ry . T he ge ne ra l d efinition of s p l i nes in t he Hilb er t s pace , - i st ence , uniquen e s s , and ch ar a c t eriz a tion t he o re ms w ere obt ain ed a b o ut 35 ye a r s ago b y M . A t t ei a , P . J . Laur en t , a n d P . M. An selon e , bu t in r e cent y e a r s important n e w r esult s h a v e b e en ob t ain ed in th e a bst ract va r i a t i o n a l s p l i ne theor y .
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.