相关论文: Discrete singular convolution and its application …

Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…

The rapid development of parallel and distributed computing paradigms has brought about great revolution in computing. Thanks to the intrinsic parallelism of evolutionary computation (EC), it is natural to implement EC on parallel and…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

We introduce and analyze a class of Galerkin-collocation discretization schemes in time for the wave equation. Its conceptual basis is the establishment of a direct connection between the Galerkin method for the time discretization and the…

Distributed algorithms to solve linear equations in multi-agent networks have attracted great research attention and many iteration-based distributed algorithms have been developed. The convergence speed is a key factor to be considered for…

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…

The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while…

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…

The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…

Tackling unsupervised source separation jointly with an additional inverse problem such as deconvolution is central for the analysis of multi-wavelength data. This becomes highly challenging when applied to large data sampled on the sphere…

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…

Clustering algorithms have significantly improved along with Deep Neural Networks which provide effective representation of data. Existing methods are built upon deep autoencoder and self-training process that leverages the distribution of…

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…