相关论文: Beyond Strang: A practical assessment of some seco…
Split learning (SL) has been recently proposed as a way to enable resource-constrained devices to train multi-parameter neural networks (NNs) and participate in federated learning (FL). In a nutshell, SL splits the NN model into parts, and…
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
We present a new parallel algorithm for solving triangular systems with multiple right hand sides (TRSM). TRSM is used extensively in numerical linear algebra computations, both to solve triangular linear systems of equations as well as to…
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in…
Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
Dynamic program slicing can significantly reduce the code developers need to inspect by narrowing it down to only a subset of relevant program statements. However, despite an extensive body of research showing its usefulness, dynamic…
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov--Galerkin method…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
It is common in classical mechanics to encounter systems whose Hamiltonian $H$ is the sum of an often exactly integrable Hamiltonian $H_0$ and a small perturbation $\epsilon H_1$ with $\epsilon\ll1$. Such near-integrability can be exploited…
We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+B(u)$ where $A$ is a linear operator and $B$ is quadratic. A particular example is the Korteweg-de Vries (KdV) equation $u_t-u u_x+u_{xxx}=0$. We…
We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm…
High order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but…
We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It…