相关论文: Stable rank-adaptive Dynamically Orthogonal Runge-…

This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

Explicit Runge-Kutta (RK) integration of hyperbolic initial-boundary value problems with time-dependent Dirichlet data often displays order reduction: the observed convergence order falls below the nominal order because the stage structure…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this…

We study the construction and convergence of semi-explicit and iterative decoupling schemes for an elliptic-parabolic problem using higher-order Runge-Kutta methods. For the semi-explicit schemes, which are constructed using a nearby delay…

This study focuses on the development and analysis of a group of high-order implicit-explicit (IMEX) Runge--Kutta (RK) methods that are suitable for discretizing gradient flows with nonlinearity that is Lipschitz continuous. We demonstrate…

Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques…

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…

We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK)…

In this paper, authors successfully construct a new algorithm for the new higher order scheme of weak approximation of SDEs. The algorithm presented here is based on [1][2]. Although this algorithm shares some features with the algorithm…

This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…

We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method. When the function is smooth…

This paper proposes the Doubly Compressed Momentum-assisted stochastic gradient tracking algorithm $\texttt{DoCoM}$ for communication-efficient decentralized optimization. The algorithm features two main ingredients to achieve a…

A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the unsteady case. Central to the framework is an optimization…

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high…

A novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations is introduced. The new methods outperform existing schemes for relatively high Peclet number due to their favorable…

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and $f$-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition…

Robust federated learning aims to maintain reliable performance despite the presence of adversarial or misbehaving workers. While state-of-the-art (SOTA) robust distributed gradient descent (Robust-DGD) methods were proven theoretically…