Optimal-order convergence of Nesterov acceleration for linear ill-posed problems
Numerical Analysis
2021-07-07 v1 Numerical Analysis
Abstract
We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a priori stopping rule and for the discrepancy principle. The essential tool to obtain this result is a representation of the residual polynomials via Gegenbauer polynomials.
Cite
@article{arxiv.2101.08168,
title = {Optimal-order convergence of Nesterov acceleration for linear ill-posed problems},
author = {Stefan Kindermann},
journal= {arXiv preprint arXiv:2101.08168},
year = {2021}
}