数值分析

Computing matrix pseudospectra over a prescribed region requires evaluating the smallest singular value of $C-zI$ at a large number of grid points, which can be prohibitively expensive for large-scale matrices. We develop a recycling-based…

For a bounded linear operator acting between Banach spaces, its metric generalized inverse is the analog to the prominent Moore-Penrose inverse for operators acting between Hilbert spaces. This generalized inverse is well-defined for Banach…

Total variation diminishing (TVD) and total variation bounded (TVB) properties are crucial for controlling spurious oscillations in numerical solutions of conservation laws. In the classical Runge--Kutta (RK) discontinuous Galerkin (DG)…

This paper studies how adaptive randomized pivoting (ARP), recently introduced for matrix column subset selection, can be extended to tensors in the t-product framework. We propose two constructions. The first one, called ARP-T-CUR, applies…

Synthetic electrocardiogram (ECG) generation can support algorithm development and robustness evaluation, but simulated signals must preserve interpretable activation, recovery, and morphology properties. We present a graph-based ECG…

Many functions exhibit approximate sparsity in their coefficients with respect to a given dictionary. In recent literature, sparse approximation in such a dictionary from i.i.d. pointwise samples, underpinned by compressed sensing, has…

Solving stochastic eigenvalue problems has long been essential for informed decision-making, advancing scientific knowledge, and ensuring the reliability of engineering designs and applications. This paper underscores the need to continue…

This work proposes a framework for sampling from the Gibbs distribution of a given potential using hybrid stochastic dynamics. In this framework, two distinct sampling dynamics are run in different regions of the state space. The two…

Spline functions, particularly B-splines, play a fundamental role in approximation theory, numerical analysis, and spectral representations. Although generating function techniques are widely used in combinatorics and special function…

Physics-informed neural networks (PINNs) formulate the solution of partial differential equations as residual minimization problems over neural network parameterizations. Although highly flexible, optimization of PINNs using modern variants…

Given a matrix $A$, a matrix nearness problem seeks an $X$ that most closely approximates $A$ in the sense of minimizing $\lVert A - X\rVert$ under a variety of constraints on $X$. A generalized matrix nearness problem seeks the same but…

We consider the numerical solution of partial differential equations with coefficients that are strongly heterogeneous in space. We provide an overview of higher-order localized orthogonal decomposition (LOD) methods for the elliptic…

A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of…

Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…

We present a high-order implicit-explicit discontinuous Galerkin (IMEX-DG) solver for the compressible Euler equations to account for rotational effects within a fully compressible atmospheric framework. Time integration follows a…

In this paper, we present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations whose discretization parameters are independent of the scaling parameter $\varepsilon$. A key ingredient of our…

We propose a high-order numerical methodology for computing the ground state and time evolution of the two-dimensional Gross-Pitaevskii equation with harmonic trapping potential. The ground state is obtained by combining normalized gradient…

This work presents a weighted quadrature (WQ) method to fast assemble Galerkin matrices based on unstructured spline surfaces. The method is developed upon a particular variant of unstructured splines, namely the bicubic analysis-suitable…

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

This paper aims to employ the weak Galerkin method to solve a class of nonlinear eigenvalue problems. We proved the weak Galerkin scheme produces lower bound for the energy. Moreover, by the post-processing technique, we obtain lower bound…