Improved Convergence Rates of Windowed Anderson Acceleration for Symmetric Fixed-Point Iterations

arXiv:2311.02490v2 Announce Type: replace-cross
Abstract: This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, $x^{(k+1)}=q(x^{(k)})$. It provides the first proof that when the operator $q$ is linear and symmetric the windowed AA, which uses a sliding window of prior iterates, improves the root-linear convergence factor over the fixed-point iterations. When $q$ is nonlinear, yet has a symmetric Jacobian at a fixed point, a slightly modified AA algorithm is proved to have an analogous root-linear convergence …

abstract algorithm anderson arxiv convergence cs.na fixed-point linear math.na math.oc paper prior stat.ml studies type