  Anderson acceleration (AA) is a technique for accelerating the convergence of
fixed-point iterations. In this paper, we apply AA to a sequence of functions
and modify the norm in its internal optimization problem to the
$\mathcal{H}^{-s}$ norm, for some positive integer $s$, to bias it towards
low-frequency spectral content in the residual. We analyze the convergence of
AA by quantifying its improvement over Picard iteration. We find that AA based
on the $\mathcal{H}^{-2}$ norm is well-suited to solve fixed-point operators
derived from second-order elliptic differential operators, including the
Helmholtz equation.
