Hilbertian Kernels and Spline Functions - 1st Edition - ISBN: 9780444897183, 9781483295190

Hilbertian Kernels and Spline Functions, Volume 4

1st Edition

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Authors: M. Atteia
eBook ISBN: 9781483295190
Imprint: North Holland
Published Date: 20th November 1992
Page Count: 393
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Table of Contents

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.


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 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.


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© North Holland 1992
20th November 1992
North Holland
eBook ISBN:

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About the Authors

M. Atteia

Affiliations and Expertise

Laboratoire d'Analyse Numérique, Université Paul Sabatier, Toulouse, France