Hilbertian kernels and spline functions

✍ Scribed by Marc Atteia

• Publisher: North-Holland
• Year: 1992
• Tongue: English
• Leaves: 385
• Series: Studies in Computational Mathematics 4
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content: 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.