Related papers: A Unified Low-rank ADI Framework with Shared Linea…

We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…

Matrix-free geometric multigrid solvers for elliptic PDEs that have been discretised with Higher-order Discontinuous Galerkin (DG) methods are ideally suited to exploit state-of-the-art computer architectures. Higher polynomial degrees…

Thanks to its great potential in reducing both computational cost and memory requirements, combining sketching and Krylov subspace techniques has attracted a lot of attention in the recent literature on projection methods for linear…

Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applications. When no ground-truth trajectories are available, but one has only snapshots of data…

We discuss several strategies to implement Dykstra's projection algorithm on NVIDIA's compute unified device architecture (CUDA). Dykstra's algorithm is the central step in and the computationally most expensive part of statistical…

We design and investigate a variety of multigrid solvers for high-order local discontinuous Galerkin methods applied to elliptic interface and multiphase Stokes problems. Using the template of a standard multigrid V-cycle, we consider a…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of…

This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…

In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…

Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. With a focus on diffusion problems, we consider DG…

In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…

Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional…

This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization…

We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…

We propose a spectral solver for the Poisson equation on a square domain, achieving optimal complexity through the ultraspherical spectral method and the alternating direction implicit (ADI) method. Compared with the state-of-the-art…

The Golub-Kahan-Tikhonov method is a popular solution technique for large linear discrete ill-posed problems. This method first applies partial Golub-Kahan bidiagonalization to reduce the size of the given problem and then uses Tikhonov…

Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular…