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Hilbertian Kernels and Spline Functions
- 1st Edition, Volume 4 - June 28, 2014
- Author: M. Atteia
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 9 3 3 - 0 7 1 4 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 9 5 1 9 - 0
In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that… Read more
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Request a sales quoteIn this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type.
Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.
Hilbertian Kernels. Interpolation. Approximation of Linear Functionals. General Formulation of the Interpolation Problem. Dual Problem. Sard's Theorem. Lagrange and Newton Interpolations. Interpolation with an Infinity of Data. Interpolating and Smoothing Spline (or Schoenberg) Functions. Operations on Spline Functions. Internal and External Convergence of Spline Functions. Interpolating Functions. Smoothing Spline Functions. Spline Functions onto a Convex Set. The Primal Problem. The Dual Problem. Spline Manifolds and Linear Elasticity. B-Splines, Box Splines, Simplicial Splines. Comments. Bibliography.
- No. of pages: 393
- Language: English
- Edition: 1
- Volume: 4
- Published: June 28, 2014
- Imprint: North Holland
- Paperback ISBN: 9781493307142
- eBook ISBN: 9781483295190
MA
M. Atteia
Affiliations and expertise
Laboratoire d'Analyse Numérique, Université Paul Sabatier, Toulouse, FranceRead Hilbertian Kernels and Spline Functions on ScienceDirect