Sequential function approximation on arbitrarily distributed point sets

JOURNAL OF COMPUTATIONAL PHYSICS

卷:354

Article

Wu, Kailiang¹  Xiu, Dongbin¹ 

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

关键词: Approximation theory;    Sequential approximation;    Randomized algorithm;   

DOI  :  10.1016/j.jcp.2017.10.020

来源: Elsevier

【 摘 要 】

We present a randomized iterative method for approximating unknown function sequentially on arbitrary point set. The method is based on a recently developed sequential approximation (SA) method, which approximates a target function using one data point at each step and avoids matrix operations. The focus of this paper is on data sets with highly irregular distribution of the points. We present a nearest neighbor replacement (NNR) algorithm, which allows one to sample the irregular data sets in a near optimal manner. We provide mathematical justification and error estimates for the NNR algorithm. Extensive numerical examples are also presented to demonstrate that the NNR algorithm can deliver satisfactory convergence for the SA method on data sets with high irregularity in their point distributions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free