相关论文: A different view on third and fourth order efficie…
The nonlinear response of stochastic models obeying a master equation is calculated up to fifth-order in the external field thus extending the third-order results obtained earlier (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012)). For…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian ($D^3f(x)\cdot d$) can be calculated at a cost proportional to that of a…
To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…
Transformers have been successfully used in various fields and are becoming the standard tools in computer vision. However, self-attention, a core component of transformers, has a quadratic complexity problem, which limits the use of…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
It is well known that finding a global optimum is extremely challenging for nonconvex optimization. There are some recent efforts \cite{anandkumar2016efficient, cartis2018second, cartis2020sharp, chen2019high} regarding the optimization…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce…
In this paper we present FASE (Fast Asynchronous Systems Evaluation), a tool for evaluating worst-case efficiency of asynchronous systems. This tool implements some well-established results in the setting of a timed CCS-like process…
In this work, we introduce a new three-dimensional chaotic differential dynamical system. We find equilibrium points of this system and provide the stability conditions for various fractional orders. Numerical simulations will be used to…
Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
Finite-difference methods are widely used for zeroth-order optimization in settings where gradient information is unavailable or expensive to compute. These procedures mimic first-order strategies by approximating gradients through function…
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…