相关论文: Direction splitting of $\varphi$-functions in expo…

The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…

We present a scalable approach to computing nonlinear balancing energy functions for control-affine systems with polynomial nonlinearities. Al'brekht's power-series method is used to solve the Hamilton-Jacobi-Bellman equations for…

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…

We show, that the Complex Step approximation to the Fr\'echet derivative of real matrix functions is applicable to the matrix sign, square root and polar mapping using iterative schemes. While this property was already discovered for the…

We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS)…

In this paper we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schroedinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is…

Several studies have shown the ability of natural gradient descent to minimize the objective function more efficiently than ordinary gradient descent based methods. However, the bottleneck of this approach for training deep neural networks…

We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…

The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

We present here a new splitting method to solve Lyapunov equations of the type $AP + PA^T=-BB^T$ in a Kronecker product form. Although that resulting matrix is of order $n^2$, each iteration of the method demands only two operations with…

The computation of approximating e^tA B, where A is a large sparse matrix and B is a rectangular matrix, serves as a crucial element in numerous scientific and engineering calculations. A powerful way to consider this problem is to use…

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable…

We investigate the possibility of constructing exponentially localized composite Wannier bases, or equivalently smooth periodic Bloch frames, for 3-dimensional time-reversal symmetric topological insulators, both of bosonic and of fermionic…

A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn-Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space…

We present in this paper two different classes of general $K$-splitting algorithms for solving finite-dimensional convex optimization problems. Under the assumption that the function being minimized has a Lipschitz continuous gradient, we…

Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional…