Spline approximation of discontinuous multivariate functions from scattered data

M. C. Lopez de Silanes; M. C. Parra; M. Pasadas; J. J. Torrens

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Spline approximation of discontinuous multivariate functions from scattered data

机译：离散数据中不连续多元函数的样条近似

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The approximation of discontinuous multivariate functions from a set of scattered data points is usually a two-stage process: first, a detection algorithm is applied to localize the discontinuity sets, then the functions are reconstructed using a fitting method. In this paper we propose a new method for the second stage, based on the computation of discrete smoothing D~m-splines. We establish a result of local convergence of the approximations provided by the method. Finally, we give some numerical and graphical examples.

机译：从一组分散的数据点中逼近不连续多元函数通常是一个两阶段过程：首先，应用检测算法对不连续集进行定位，然后使用拟合方法重构这些函数。在本文中，我们基于离散平滑D〜m样条的计算，提出了一种用于第二阶段的新方法。我们建立了该方法提供的近似值的局部收敛结果。最后，我们给出一些数字和图形示例。

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《Journal of Computational and Applied Mathematics》 |2001年第2期|共18页
作者
M. C. Lopez de Silanes; M. C. Parra; M. Pasadas; J. J. Torrens;
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正文语种 eng
中图分类应用数学;
关键词
discontinuous functions; fitting method; discrete smoothing D~m-splines; local convergence;

机译：不连续函数拟合方法离散平滑D〜m样条局部收敛;

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专利

1. Spline approximation of discontinuous multivariate functions from scattered data [J] . M. C. Lopez de Silanes, M. C. Parra, M. Pasadas, Journal of Computational and Applied Mathematics . 2001,第1a2期

机译：离散数据中不连续多元函数的样条近似
2. Approximation of Discontinuous Function of Two Variables by Approximating Discontinuous Bilinear Spline Using the Least Squares Method(Rectangular Elements) [J] . O.N. Lytvyn, Yu.I. Pershina Journal of automation and information sciences . 2012,第5期

机译：用最小二乘法（矩形元素）逼近不连续双线性样条，逼近两个变量的不连续函数
3. Numerical integration on multivariate scattered data by Lobachevsky splines [J] . Giampietro Allasia, Roberto Cavoretto, Alessandra De Rossi International journal of computer mathematics . 2013,第9a10期

机译：Lobachevsky样条对多元分散数据的数值积分
4. Fast Polynomial Spline Approximation for Large Scattered Data Sets via L_1 Minimization [C] . Laurent Gajny, Eric Nyiri, Olivier Gibaru International conference on geometric science of information . 2013

机译：通过L_1最小化对大型散乱数据集进行快速多项式样条逼近
5. Multivariate Spline Method for Scattered Data Fitting, Curve and Surface Reconstruction, and Numerical Solution to Poisson Equations via Domain Decomposition Method [D] . Xu, Yidong . 2019

机译：散射数据拟合，曲线和表面重建的多变量样条方法，以及通过域分解法的泊松方程的数值解
6. Multivariate Test Power Approximations for Balanced Linear Mixed Models in Studies with Missing Data [O] . Brandy M. Ringham, Sarah M. Kreidler, Keith E. Muller, -1

机译：缺失数据研究中平衡线性混合模型的多元测试功效逼近
7. Spline approximation of discontinuous multivariate functions from scattered data [O] . López de Silanes M.C., Parra M.C., Pasadas M., 2001

机译：离散数据中不连续多元函数的样条近似
8. Radial basis functions: A class of grid-free, scattered data approximations. [R] . E. J. Kansa R. E. Carlson 1992

机译：径向基函数：一类无网格，分散的数据近似。

Spline approximation of discontinuous multivariate functions from scattered data

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