Dr. Teng Zhang will be speaking at this seminar about improved convergence rates of Anderson acceleration for a large class of fixed-point iterations.

Abstract: This talk studies Anderson acceleration (AA) for fixed-point methods. It provides the first proof that when the operator q is linear and symmetric, AA improves the root-linear convergence factor over the fixed-point iterations. When q is nonlinear, yet has a symmetric Jacobian at the solution, a slightly modified AA algorithm is proved to have an analogous root-linear convergence factor improvement over fixed-point iterations. Simulations verify our observations. Furthermore, experiments with different data models demonstrate AA is significantly superior to the standard fixed-point methods for Tyler's M-estimation.

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