相关论文: Cross-points in the Neumann-Neumann method

We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…

We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting…

In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear…

This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…

We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…

We propose a modified normalized direct linear transform (DLT) algorithm for solving the perspective-n-point (PnP) problem with much better behavior than the conventional DLT. The modification consists of analytically weighting the…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…

We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks. The field solution on each…

Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…

We present Nystr\"om discretizations of multitrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

We present a Waveform Relaxation (WR) version of the Neumann-Neumann algorithm for the wave equation in space-time. The method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves in…

Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when…

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods…

The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimization problem on the Stiefel manifold that can be solved using…

Our work proposes a unified approach to three different topics in a general Riemannian setting: splitting theorems, symmetry results and overdetermined elliptic problems. By the existence of a stable solution to the semilinear equation…