Related papers: AA-ICP: Iterative Closest Point with Anderson Acce…
In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
This paper proposes an effective approach for the scaling registration of $m$-D point sets. Different from the rigid transformation, the scaling registration can not be formulated into the common least square function due to the ill-posed…
We present a novel approach for accelerating AI performance by leveraging Anderson extrapolation, a vector-to-vector mapping technique based on a window of historical iterations. By identifying the crossover point (Fig. 1) where a mixing…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for the incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ penalty parameter, and Anderson acceleration (AA) is used to…
We present a simple way to learn a transformation that maps samples of one distribution to the samples of another distribution. Our algorithm comprises an iteration of 1) drawing samples from some simple distribution and transforming them…
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 $\mathcal{H}^{-s}$…
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…
In this paper, we introduce a new iteration method and show that this iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that the new iteration method is equivalent to both Mann…
Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a least squares problem at each iteration and a reliance on…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…
Two adaptive relaxation strategies are proposed for Anderson acceleration. They are specifically designed for applications in which mappings converge to a fixed point. Their superiority over alternative Anderson acceleration is demonstrated…
Anderson mixing (AM) is a classical method that can accelerate fixed-point iterations by exploring historical information. Despite the successful application of AM in scientific computing, the theoretical properties of AM are still under…
In this paper we present a new iterative projection method for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method, termed AAMR for averaged alternating modified reflections,…
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…
Anderson acceleration (AA) is an extrapolation technique designed to speed-up fixed-point iterations like those arising from the iterative training of DL models. Training DL models requires large datasets processed in randomly sampled…
The accelerated proximal point algorithm (APPA), also known as "Catalyst", is a well-established reduction from convex optimization to approximate proximal point computation (i.e., regularized minimization). This reduction is conceptually…
In the Canadian's lumber industry, simulators are used to predict the lumbers resulting from the sawing of a log at a given sawmill. Giving a log or several logs' 3D scans as input, simulators perform a real-time job to predict the lumbers.…