Related papers: A tensor Alternating Anderson-Richardson method fo…
The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi {\it et al.} [Numer. Algorithms; 84 (2) (2020) 457-483], recently. The authors…
Anderson Acceleration is a well-established method that allows to speed up or encourage convergence of fixed-point iterations. It has been successfully used in a variety of applications, in particular within the Self-Consistent Field (SCF)…
In this paper, the Newton-Anderson method, which results from applying an extrapolation technique known as Anderson acceleration to Newton's method, is shown both analytically and numerically to provide superlinear convergence to non-simple…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
In this paper we propose an algorithm to classify tensor data. Our methodology is built on recent studies about matrix classification with the trace norm constrained weight matrix and the tensor trace norm. Similar to matrix classification,…
The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the…
In this paper, we propose and analyze iterative method based on projection techniques to solve a non-singular linear system Ax = b. In particular, for a given positive integer m, m-dimensional successive projection method (mD-SPM) for…
We consider the tensor equation whose coefficient tensor is a nonsingular M-tensor and whose right side vector is nonnegative. Such a tensor equation may have a large number of nonnegative solutions. It is already known that the tensor…
The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…
This paper applies the Anderson Acceleration (AA) technique to accelerate the Fenchel dual gradient method (FDGM) to solve constrained optimization problems over time-varying networks. AA is originally designed for accelerating fixed-point…
The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of…
The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As…
We consider two modifications of the Arrow-Hurwicz (AH) iteration for solving the incompressible steady Navier-Stokes equations for the purpose of accelerating the algorithm: grad-div stabilization, and Anderson acceleration. AH is a…
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 propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…
Partitioning large machine learning models across distributed accelerator systems is a complex process, requiring a series of interdependent decisions that are further complicated by internal sharding ambiguities. Consequently, existing…
We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
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,…
Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introduce the Richardson(m) neural solver by employing a meta…