Related papers: Norm-based convergence bounds for nonsymmetric alg…

In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid…

In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and…

When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use…

Since its invention in 2014, the Adam optimizer has received tremendous attention. On one hand, it has been widely used in deep learning and many variants have been proposed, while on the other hand their theoretical convergence property…

We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…

This paper makes the following original contributions. First, we develop a unifying framework for testing shape restrictions based on the Wald principle. The test has asymptotic uniform size control and is uniformly consistent. Second, we…

We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…

We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…

We present novel improvements in the context of symbol-based multigrid procedures for solving large block structured linear systems. We study the application of an aggregation-based grid transfer operator that transforms the symbol of a…

In machine learning, asynchronous parallel stochastic gradient descent (APSGD) is broadly used to speed up the training process through multi-workers. Meanwhile, the time delay of stale gradients in asynchronous algorithms is generally…

We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD…

We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…

We consider the linear system Ax=b arising from one-dimensional Poisson's equation with Dirichlet boundary conditions, where A is the square matrix with the stencil form [-1 2 -1]. Here we show that a pairwise aggregation-based algebraic…

We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…

The class of absolutely norming operators on complex Hilbert spaces of arbitrary dimensions was introduced in [6] and a spectral characterization theorem for these operators was established in [11]. In this paper we extend the concept of…

We propose a novel algorithmic framework of Variable Metric Over-Relaxed Hybrid Proximal Extra-gradient (VMOR-HPE) method with a global convergence guarantee for the maximal monotone operator inclusion problem. Its iteration complexities…

In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…

We introduce a homogeneous multigrid method in the sense that it uses the same HDG discretization scheme for Poisson's equation on all levels. In particular, we construct a stable injection operator and prove optimal convergence of the…