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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,…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
Anderson acceleration is an old and simple method for accelerating the computation of a fixed point. However, as far as we know and quite surprisingly, it has never been applied to dynamic programming or reinforcement learning. In this…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
We consider the problem of nonnegative tensor completion. We adopt the alternating optimization framework and solve each nonnegative matrix completion problem via a stochastic variation of the accelerated gradient algorithm. We…
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…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
There is currently an increasing interest in developing efficient solvers for phase-field modeling of brittle fracture. The governing equations for this problem originate from a constrained minimization of a non-convex energy functional,…
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…
Anderson acceleration (AA) is a well-known method for accelerating the convergence of iterative algorithms, with applications in various fields including deep learning and optimization. Despite its popularity in these areas, the…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…
Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…
Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the convergence behavior of a corresponding fixed-point residual, while…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteration of Anderson acceleration. The filtering strategy consists…
In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm…
Anderson Acceleration (AA) is a popular algorithm designed to enhance the convergence of fixed-point iterations. In this paper, we introduce a variant of AA based on a Truncated Gram-Schmidt process (AATGS) which has a few advantages over…