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Sparse Data Interpolation and Smoothing on Embedded Submanifolds
Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2020-07-10 , DOI: 10.1007/s10915-020-01268-z
L.-B. Maier

Energy minimization is one of the properties that make univariate splines so favorable in many problems of approximation and estimation; interpolation in and extrapolation from sparse data sites and smoothing of noisy data in particular. In this paper, we present a novel approach to approximate energy minimization on certain classes of submanifolds that gives rise to new methods for extrapolation and smoothing on submanifolds. To accomplish this, we minimize intrinsic functionals approximately by minimising a suitable extrinsic formulation of the functional augmented by a penalty on the first order normal derivative. The general framework we develop is accompanied by error analysis and exemplified by tensor product B-splines.



中文翻译:

嵌入式子流形上的稀疏数据插值和平滑

能量最小化是使单变量样条在许多逼近和估计问题中如此受欢迎的特性之一;稀疏数据站点的内插和外推,尤其是噪声数据的平滑。在本文中,我们提出了一种新颖的方法来近似估计某些子流形上的能量最小化,从而产生了用于子流形外推和平滑的新方法。为实现此目的,我们通过最小化一阶正态导数的罚分来增强功能的适当外部形式,从而使内部功能性最小化。我们开发的一般框架伴随着错误分析,并以张量积B样条为例。

更新日期:2020-07-10
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