Related papers: Reduced Collocation Methods: Reduced Basis Methods…
This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
An isogeometric approach for solving the Laplace-Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull-Clark subdivision surfaces is presented and assessed. The…
We consider linear dynamical systems of ordinary differential equations or differential algebraic equations. Physical parameters are substituted by random variables for an uncertainty quantification. We expand the state variables as well as…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
For planning rearrangements of objects in a clutter, it is required to know the goal configuration of the objects. However, in real life scenarios, this information is not available most of the time. We introduce a novel method that…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…
We consider the problem of solving linear least squares problems in a framework where only evaluations of the linear map are possible. We derive randomized methods that do not need any other matrix operations than forward evaluations,…
Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with…
The analysis of second-order optimization methods based either on sub-sampling, randomization or sketching has two serious shortcomings compared to the conventional Newton method. The first shortcoming is that the analysis of the iterates…
Recently, it has been shown that approximations to marginal posterior distributions obtained using a low discrepancy sequence (LDS) can outperform standard grid-based methods with respect to both accuracy and computational efficiency. This…
The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a…
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…
This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small correlation lengths. The presented method is based on a…
The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…
In this work, we develop a distributed least squares approximation (DLSA) method that is able to solve a large family of regression problems (e.g., linear regression, logistic regression, and Cox's model) on a distributed system. By…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
We present the Stochastic alternate Linearization Method (StochaLM), a token-based method for distributed optimization. This algorithm finds the solution of a consensus optimization problem by solving a sequence of subproblems where some…