通过基于块的搜索技术高效计算分区统一插值项
Efficient computation of partition of unity interpolants through a block-based searching technique
AI总结：
本文提出一种高效插值工具，适用于大规模散乱数据集。通过将径向基函数作为局部近似函数，并使用局部支持权重函数，结合基于块的空间划分数据结构，优化了最近邻点搜索过程，通过二维和三维插值的复杂度分析和数值实验验证了方法的有效性，并讨论了用于几何建模的应用及Matlab软件包。
摘要：
在本文中，我们提出了一种新的高效插值工具，特别适用于大规模散乱数据集。所采用的分区统一方法通过混合径向基函数（RBFs）作为局部近似函数，并使用局部支持权重函数进行处理。特别地，我们提出了一种基于块的空间划分数据结构，该结构基于对底层通用域进行分块。这种方法允许在最近邻点搜索过程中仅检查少量的块，从而实现优化的搜索过程。二维和三维插值的复杂度分析和数值实验支持了我们的发现。还考虑了一些几何建模的应用。此外，还讨论了用Matlab编写的关联软件包，并将其提供给科学界。
英文摘要：
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weight functions. In particular we present a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerical experiments in two- and three-dimensional interpolation support our findings. Some applications to geometric modelling are also considered. Moreover, the associated software package written in \textsc{Matlab} is here discussed and made available to the scientific community.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
