Gradient Descent-based D-optimal Design for the Least-Squares Polynomial Approximation
Numerical Analysis
2018-10-03 v2
Abstract
In this work, we propose a novel sampling method for Design of Experiments. This method allows to sample such input values of the parameters of a computational model for which the constructed surrogate model will have the least possible approximation error. High efficiency of the proposed method is demonstrated by its comparison with other sampling techniques (LHS, Sobol' sequence sampling, and Maxvol sampling) on the problem of least-squares polynomial approximation. Also, numerical experiments for the Lebesgue constant growth for the points sampled by the proposed method are carried out.
Cite
@article{arxiv.1806.06631,
title = {Gradient Descent-based D-optimal Design for the Least-Squares Polynomial Approximation},
author = {V. P. Zankin and G. V. Ryzhakov and I. V. Oseledets},
journal= {arXiv preprint arXiv:1806.06631},
year = {2018}
}
Comments
17 pages