no code implementations • 29 Sep 2021 • Hans De Sterck, Yunhui He, Oliver A. Krzysik
As a roadway towards gaining more understanding of convergence acceleration by AA, we study AA($m$), i. e., Anderson acceleration with finite window size $m$, applied to the case of linear fixed-point iterations $x_{k+1}=M x_{k}+b$.
no code implementations • 29 Sep 2021 • Hans De Sterck, Yunhui He
However, we show that, despite the discontinuity of $\beta(z)$, the iteration function $\Psi(z)$ is Lipschitz continuous and directionally differentiable at $z^*$ for AA(1), and we generalize this to AA($m$) with $m>1$ for most cases.
1 code implementation • 6 Jul 2020 • Da-Wei Wang, Yunhui He, Hans De Sterck
In this paper we explain and quantify this improvement in linear asymptotic convergence speed for the special case of a stationary version of AA applied to ADMM.
1 code implementation • 4 Jul 2020 • Hans De Sterck, Yunhui He
Since AA and NGMRES are equivalent to GMRES in the linear case, one may expect the GMRES convergence factors to be relevant for AA and NGMRES as $x_k \rightarrow x^*$.