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

Anderson Acceleration Based on the $\mathcal{H}^{-s}$ Sobolev Norm for Contractive and Noncontractive Fixed-Point Operators