相关论文: Structural Convergence Results for Approximation o…

Diagonally dominant matrices have many applications in systems and control theory. Linear dynamical systems with scaled diagonally dominant drift matrices, which include stable positive systems, allow for scalable stability analysis. For…

The goal of the paper is to introduce a convergence \`a la Gromov-Hausdorff for Lorentzian spaces, building on $\epsilon$-nets consisting of causal diamonds and relying only on the time separation function. This yields a geometric notion of…

The problem of Anderson localization, as well as the single particle localization-delocalizaton transition of the Aubry-Andr\'e model, is studied employing operator Krylov space methods. It is shown that even when the dynamics is generated…

Our goal is to establish what seems to be the first rigidity result for CR embeddings between Shilov boundaries of bounded symmetric domains of higher rank. The result states that any such CR embedding is the standard linear embedding up to…

We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix $A$, defined as $\operatorname{tr}(f(A))$ where $f(x)=-x\log x$. After establishing some useful properties of this…

We study the problem of distance-based formation control in autonomous multi-agent systems in which only distance measurements are available. This means that the target formations as well as the sensed variables are both determined by…

We use the intrinsic area to define a distance on the space of homothety classes of convex bodies in the $n$-dimensional Euclidean space, which makes it isometric to a convex subset of the infinite dimensional hyperbolic space. The ambient…

The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…

This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems. The…

Frequent Directions, as a deterministic matrix sketching technique, has been proposed for tackling low-rank approximation problems. This method has a high degree of accuracy and practicality, but experiences a lot of computational cost for…

Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…

The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear…

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a…

In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…

We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…

We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In particular, we demonstrate that several recently proposed RBMs…

A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an $N$-dimensional hyperrectangle. In particular, it is shown that these functions can be expressed in terms of their highest-order mixed…

Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…

Empirical studies reported that the Hessian matrix of neural networks (NNs) exhibits a near-block-diagonal structure, yet its theoretical foundation remains unclear. In this work, we reveal that the reported Hessian structure comes from a…

We propose a novel Krylov subspace method for estimating the finite impulse response (FIR) of a one-dimensional linear time-invariant systems. The method approximates the system's FIR using a kernel-based formulation combined with…