Related papers: Shanks and Anderson-type acceleration techniques f…
Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a novel optimization algorithm by adapting Anderson…
In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a…
In this paper, we propose a novel Anderson's acceleration method to solve nonlinear equations, which does \emph{not} require a restart strategy to achieve numerical stability. We propose the greedy and random versions of our algorithm.…
This paper primarily presents numerical results for the Anderson accelerated Newton method on a set of benchmark problems. The results demonstrate superlinear convergence to solutions of both degenerate and nondegenerate problems. The…
In this report, we present a versatile and efficient preconditioned Anderson acceleration (PAA) method for fixed-point iterations. The proposed framework offers flexibility in balancing convergence rates (linear, super-linear, or quadratic)…
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 $\mathcal{H}^{-s}$…
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of…
This work investigates the local convergence behavior of Anderson acceleration in solving nonlinear systems. We establish local R-linear convergence results for Anderson acceleration with general depth $m$ under the assumptions that the…
We propose, analyze and test Anderson-accelerated Picard iterations for solving the incompressible Navier-Stokes equations (NSE). Anderson acceleration has recently gained interest as a strategy to accelerate linear and nonlinear…
In this paper a family of fixed point algorithms, generalizing the \PM method, is considered. A previous work studied the convergence of the methods. Presented here is a second part of the analysis, concerning the introduction of some…
The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application…
Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) \triangleq x-\alpha\nabla f(x)$. It…
This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson…
The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to-implement nonlinear preconditioning of Newton's iteration,…
In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice…
In this work, we extend a modified Anderson acceleration proposed in [Y. He, arXiv:2603.25983, 2026] to accelerate the Picard iteration for the Navier-Stokes equations. In this variant of Anderson acceleration, named AAg, the nonlinear…
We give a complete characterization of the behavior of the Anderson acceleration (with arbitrary nonzero mixing parameters) on linear problems. Let n be the grade of the residual at the starting point with respect to the matrix defining the…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
This paper provides the first proof that Anderson acceleration (AA) improves the convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlinear solvers in many applications, however a rigorous…
For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements…