Related papers: A low-rank, high-order implicit-explicit integrato…

Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…

Differential algebraic Riccati equations are at the heart of many applications in control theory. They are time-depent, matrix-valued, and in particular nonlinear equations that require special methods for their solution. Low-rank methods…

Discrete regularization methods are often applied for obtaining stable approximate solutions for ill-posed operator equations $Tx=y$, where $T: X\to Y$ is a bounded operator between Hilbert spaces with non-closed range $R(T)$ and $y\in…

In this study we consider unconditionally non-oscillatory, high order implicit time marching based on time-limiters. The first aspect of our work is to propose the high resolution Limited-DIRK3 (L-DIRK3) scheme for conservation laws and…

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six--dimensional phase space, making simulations of…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…

The numerical solution of algebraic tensor equations is a largely open and challenging task. Assuming that the operator is symmetric and positive definite, we propose two new gradient-descent type methods for tensor equations that…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

In this paper, in order to improve the spatial accuracy, the exponential integrator Fourier Galerkin method (EIFG) is proposed for solving semilinear parabolic equations in rectangular domains. In this proposed method, the spatial…

We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…

We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…

In this paper, two novel classes of implicit exponential Runge-Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, we analyze the symplectic conditions of two kinds of exponential integrators, and present a…

In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit-implicit-null (EIN) method to separate the nonlinear term into a linear term and a damping term, and…

This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…

Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…