相关论文: Beyond Strang: A practical assessment of some seco…
For linear differential equations of the form $u'(t)=[A + B(t)] u(t)$, $t\geq0$, with a possibly unbounded operator $A$, we construct and deduce error bounds for two families of second-order exponential splittings. The role of quadratures…
Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to…
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…
Division algorithms have been developed to reduce latency and to improve the efficiency of the processors. Floating point division is considered as a high latency operation. This papers looks into one such division algorithm, examines the…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
We propose a short-memory operator splitting scheme for solving the constant-Q wave equation, where the fractional stress-strain relation contains multiple Caputo fractional derivatives with order much smaller than 1. The key is to exploit…
We consider distributed optimization problems in which a group of agents are to collaboratively seek the global optimum through peer-to-peer communication networks. The problem arises in various application areas, such as resource…
We introduce an inertial variant of the forward-Douglas-Rachford splitting and analyze its convergence. We specify an instance of the proposed method to the three-composite convex minimization template. We provide practical guidance on the…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
Constraint problems can be trivially solved in parallel by exploring different branches of the search tree concurrently. Previous approaches have focused on implementing this functionality in the solver, more or less transparently to the…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
We study the convergence of the Left-Right splitting method (equivalent in key respects to the Method of Multiple Ordered Interactions and Forward-Backward method) for wave scattering by rough surfaces. This is an operator series method…
This article presents an overview of a research study of a crucial optimization problem in the Computer Science/Operations research field: The Job-shop Scheduling Problem (JSP). The JSP is a challenging task in which a set of operations…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
For solving a class of block two-by-two real linear system, a new single-step iteration method based on triangular splitting scheme is proposed in this paper. Then the convergence properties of this method are carefully investigated. In…
This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is…
The widespread adoption of distributed learning to train a global model from local data has been hindered by the challenge posed by stragglers. Recent attempts to mitigate this issue through gradient coding have proved difficult due to the…