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" Variational Theory of Splines "
by Anatoly Yu. Bezhaev, Vladimir A. Vasilenko.
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BL
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| Record Number
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621255
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dltt
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| Main Entry
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Bezhaev, Anatoly Yu.
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| Title & Author
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Variational Theory of Splines\ by Anatoly Yu. Bezhaev, Vladimir A. Vasilenko.
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| Publication Statement
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Boston, MA :: Springer US :: Imprint: Springer,, 2001.
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| ISBN
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9781475734287
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: 9781441933683
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| Contents
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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.
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| Abstract
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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 .
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Mathematics.
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Electronic data processing.
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Global analysis (Mathematics).
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Functional analysis.
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Mathematical optimization.
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| Added Entry
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Vasilenko, Vladimir A.
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SpringerLink (Online service)
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