Splines on Manifolds

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
Chapter

Abstract

In the present chapter, we propose a method of solving approximation problems for functions defined on manifolds in ℝ n by using D m -spline traces onto the manifolds. For the sake of simplicity, we confine ourselves to the case of (n — 1)-dimensional smooth manifolds in ℝn, which are boundaries of simply connected bounded domains. In Section 6.1, an analysis is given of existence and uniqueness of traces of interpolating Dm-splines and, also, of their convergence (convergence orders) in the case of condensed grids of interpolation nodes on a manifold.

Keywords

Variational Theory Sobolev Function Algebraic Manifold Prescribe Point Dimensional Smooth Manifold 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
    • 1
  1. 1.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirskRussia

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