Sequential function approximation with noisy data

JOURNAL OF COMPUTATIONAL PHYSICS

卷:371

Article

Shin, Yeonjong¹  Wu, Kailiang¹  Xiu, Dongbin¹ 

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

关键词: Approximation theory;    Randomized algorithm;    Noisy data;   

DOI  :  10.1016/j.jcp.2018.05.042

来源: Elsevier

【 摘 要 】

We present a sequential method for approximating an unknown function sequentially using random noisy samples. Unlike the traditional function approximation methods, the current method constructs the approximation using one sample at a time. This results in a simple numerical implementation using only vector operations and avoids the need to store the entire data set. The method is thus particularly suitable when data set is exceedingly large. Furthermore, we present a general theoretical framework to define and interpret the method. Both upper and lower bounds of the method are established for the expectation of the results. Numerical examples are provided to verify the theoretical findings. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free