Related papers: A parallel rank-adaptive integrator for dynamical …
In this work we investigate the parallel scalability of the numerical method developed in Guthrey and Rossmanith [The regionally implicit discontinuous Galerkin method: Improving the stability of DG-FEM, SIAM J. Numer. Anal. (2019)]. We…
In this paper, we present a new variational integrator for problems in Lagrangian mechanics. Using techniques from Galerkin variational integrators, we construct a scheme for numerical integration that converges geometrically, and is…
The numerical solution of parameter identification inverse problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank scheme for the reconstruction of the scattering…
We introduce a method that uses low-rank approximations of cross-correlation matrices in mixed continuous and categorical Gaussian Process models. This new method -- called Low-Rank Correlation (LRC) -- offers the ability to flexibly adapt…
In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introduce a geometric description of the set of fixed rank matrices…
CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…
In this work, we introduce a quadratically convergent and dynamically consistent integrator specifically designed for the replicator dynamics. The proposed scheme combines a two-stage rational approximation with a normalization step to…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
Fully parallel architecture at disparity-level for efficient semi-global matching (SGM) with refined rank method is presented. The improved SGM algorithm is implemented with the non-parametric unified rank model which is the combination of…
Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal…
We present a distributed asynchronous algorithm for approximating a single component of the solution to a system of linear equations $Ax = b$, where $A$ is a positive definite real matrix, and $b \in \mathbb{R}^n$. This is equivalent to…
In this paper, we present a predictor-corrector strategy for constructing rank-adaptive dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear…
We introduce a reformulation of regularized low-rank recovery models to take advantage of GPU, multiple CPU, and hybridized architectures. Low-rank recovery often involves nuclear-norm minimization through iterative thresholding of singular…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision…
A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov-Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs' systems in a continuous setting, it combines recently…
We consider the problem of computing tractable approximations of time-dependent d x d large positive semi-definite (PSD) matrices defined as solutions of a matrix differential equation. We propose to use "low-rank plus diagonal" PSD…