相关论文: Sharpened PCG Iteration Bound for High-Contrast He…

Learning-based point cloud compression presents superior performance to handcrafted codecs. However, pretrained-based methods, which are based on end-to-end training and expected to generalize to all the potential samples, suffer from…

In this work, we develop proximal preconditioned gradient methods with a focus on spectral gradient methods providing a proximal extension to the Muon and Scion optimizers. We introduce a family of stochastic algorithms that can handle a…

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…

Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in…

We deal with the numerical solution of linear elliptic problems with varying diffusion coefficient by the $hp$-discontinuous Galerkin method. We develop a two-level hybrid Schwarz preconditioner for the arising linear algebraic systems. The…

A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…

Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…

We present a framework for upper bounding the number of iterations required by first-order optimization algorithms implementing constrained LQR controllers. We derive new bounds for the condition number and extremal eigenvalues of the…

We consider the setting of distributed empirical risk minimization where multiple machines compute the gradients in parallel and a centralized server updates the model parameters. In order to reduce the number of communications required to…

We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained…

We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…

In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the…

In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for $K \times N$ sub-systems connected in a two-dimensional (2D) grid…

Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a…

In this paper, we present a parallel higher-order boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov…

Automatic detection of phoneme or word-like units is one of the core objectives in zero-resource speech processing. Recent attempts employ self-supervised training methods, such as contrastive predictive coding (CPC), where the next frame…

Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such…