相关论文: Should exponential integrators be used for advecti…

An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on…

We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…

Exact methods for exponentiation of matrices of dimension $N$ can be computationally expensive in terms of execution time ($N^{3}$) and memory requirements ($N^{2}$) not to mention numerical precision issues. A type of matrix often…

The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex…

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

In recent years, a great deal of attention has been focused on numerically solving exponential integrators. The important ingredient to the implementation of exponential integrators is the efficient and accurate evaluation of the so called…

We consider the adaptive-rank integration of {2D and 3D} time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled…

This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be…

We change a previous time-stepping algorithm for solving a multi-scale Vlasov-Poisson system within a Particle-In-Cell method, in order to do accurate long time simulations. As an exponential integrator, the new scheme allows to use large…

The computation of the Log-determinant of large, sparse, symmetric positive definite (SPD) matrices is essential in many scientific computational fields such as numerical linear algebra and machine learning. In low dimensions, Cholesky is…

In this paper we investigate some practical aspects concerning the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. We derive some…

Developing large-scale distributed methods that are robust to the presence of adversarial or corrupted workers is an important part of making such methods practical for real-world problems. In this paper, we propose an iterative approach…

Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…

Derivative based optimization methods are efficient at solving optimal control problems near local optima. However, their ability to converge halts when derivative information vanishes. The inference approach to optimal control does not…

In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more…

In this paper, two novel classes of implicit exponential Runge-Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, we analyze the symplectic conditions of two kinds of exponential integrators, and present a…

This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…

With a recent trend of using Large Language Models (LLMs) for different applications within smart cities, there is a need for pushing these models toward the edge of network while still preserving their performance. Edge Computing (EC) as a…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

In this paper, we implement exponential integrators, specifically Integrating Factor (IF) and Exponential Time Differencing (ETD) methods, using pseudo-spectral techniques to solve phase-field equations within a Python framework. These…