Tao Hong and Irad Yavneh, ``On Adapting Nesterov’s Scheme to Accelerate Iterative Methods for Linear Problem'', Accepted to Numerical Linear Algebra with Applications, 2021.

In this paper, we propose a closed-form solution to decide the optimal parameter inside Nesterov's scheme when the eigenvalues of the iteration matrix are real and the smallest and largest eigenvalues are given. Moreover, we show a sufficient condition which explicitly depicts a complex domain that the optimal parameter obtained through the smallest and largest real eigenvalues are still optimal when the iteration matrix has complex eigenvlaues.

ArXiv Paper Link: https://arxiv.org/abs/2102.09239.

``Demo_Laplacian.m'': the demo of solving the Poisson problem.

``Fig6_DampingFactorJacobi.m'': reproduce Fig. 6 of our paper.

``Figs4and5_ChebyVSNesterACFComplexEigenvalues'': reproduce Fig.s 4 and 5 of our paper.

Please add ``utilities'' folder in your own matlab path before running the codes.

Feel free to shoot me (Tao Hong) an email: [email protected] if you find any bugs in this software or have any question regarding our paper.

https://hongtao-argmin.github.io