Related papers: Low rank approximations for the DEPOSIT computer c…
We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the…
In this work, the low rank approximation concept is extended to the non-equilibrium Green's function (NEGF) method to achieve a very efficient approximated algorithm for coherent and incoherent electron transport. This new method is applied…
In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time…
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approximation is attained if a control parameter is zero or…
Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to…
Dose calculations in proton therapy require the fast and accurate solution of a high-dimensional transport equation for a large number of (pencil) beams with different energies and directions. Deterministically solving this transport…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
(Rephrased) Non-conformance decision-making processes in high-precision manufacturing of engineering structures are often delayed due to numerical simulations that are needed for analyzing the defective parts and assemblies. Interfaces…
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better complexity with respect to the tensor rank than previous…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
We present a highly efficient molecular dynamics scheme for calculating the concentration profile of dopants implanted in group-IV alloy, and III-V zinc blende structure materials. Our program incorporates methods for reducing computational…
Dynamical low-rank approximation in the Tucker tensor format of given large time-dependent tensors and of tensor differential equations is the subject of this paper. In particular, a discrete time integration method for rank-constrained…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
Deterministic models for radiation transport describe the density of radiation particles moving through a background material. In radiation therapy applications, the phase space of this density is composed of energy, spatial position and…
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…
In modern computing units, division operations are generally slower than other arithmetic operations and require more resources, such as area and power, than multiplication. To reduce the delay, fast division algorithms use an initial…
In this paper, we propose a new lower approximation scheme for POMDP with discounted and average cost criterion. The approximating functions are determined by their values at a finite number of belief points, and can be computed efficiently…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…