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Radial basis function approximations: comparison and applications

机译：径向基函数近似：比较和应用

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摘要

Approximation of scattered data is often a task in many engineering problems. The radial basis function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher dimension d > 2, because the other methods require the conversion of a scattered dataset to an ordered dataset (i.e. a semi-regular mesh is obtained by using some tessellation techniques), which is computationally expensive. The RBF approximation is non-separable, as it is based on the distance between two points. This method leads to a solution of linear system of equations (LSE) Ac=h. In this paper several RBF approximation methods are briefly introduced and a comparison of those is made with respect to the stability and accuracy of computation. The proposed RBF approximation offers lower memory requirements and better quality of approximation.
机译：在许多工程问题中，分散数据的逼近通常是一项任务。径向基函数（RBF）近似适用于d维空间中的大型分散（无序）数据集。这种方法适用于d> 2的更高维度，因为其他方法需要将分散的数据集转换为有序的数据集（即通过使用一些细分技术获得半规则网格），这在计算上非常昂贵。 RBF近似是不可分离的，因为它基于两点之间的距离。该方法导致方程线性系统（LSE）Ac = h的解。本文简要介绍了几种RBF近似方法，并就计算的稳定性和准确性进行了比较。拟议的RBF近似值可提供较低的内存要求和更好的近似值。

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  • 来源
    《Applied Mathematical Modelling》 |2017年第11期|728-743|共16页
  • 作者

    Majdisova Zuzana; Skala Václav;

  • 作者单位

    Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, Plzen, CZ, Czech Republic;

    Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, Plzen, CZ, Czech Republic;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Approximation; Lagrange multipliers; Radial basis function; RBF;

    机译：近似;拉格朗日乘数;径向基函数;皇家空军;

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