On a near optimal sampling strategy for least squares polynomial regression

JOURNAL OF COMPUTATIONAL PHYSICS

卷:326

Article

Shin, Yeonjong¹  Xiu, Dongbin¹ 

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

关键词: Polynomial regression;    Least squares;    Christoffel function;   

DOI  :  10.1016/j.jcp.2016.09.032

来源: Elsevier

【 摘 要 】

We present a sampling strategy of least squares polynomial regression. The strategy combines two recently developed methods for least squares method: Christoffel least squares algorithm and quasi-optimal sampling. More specifically, our new strategy first choose samples from the pluripotential equilibrium measure and then re-order the samples by the quasi-optimal algorithm. A weighted least squares problem is solved on a (much) smaller sample set to obtain the regression result. It is then demonstrated that the new strategy results in a polynomial least squares method with high accuracy and robust stability at almost minimal number of samples. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free