Splines on Manifolds

Anatoly Yu. Bezhaev and Vladimir A. Vasilenko
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Vladimir A. Vasilenko: Institute of Computational Mathematics and Mathematical Geophysics

Chapter Chapter 6 in Variational Theory of Splines, 2001, pp 135-155 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-3428-7_6

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DOI: 10.1007/978-1-4757-3428-7_6

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