Variational Theory of Splines

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 .

Inhalt

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.