相关论文: Finite Difference Weerakoon-Fernando Method to sol…

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe…

In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…

Let $z_{1},z_{2},...,z_{N}$ be a sequence of distinct grid points. A finite difference formula approximates the $m$-th derivative $f^{(m)}(0)$ as $\sum w_{k}f(z_{k})$, with $w_{k}$ being the weights. We derive an algorithm for finding the…

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…

Fairness has emerged as a critical problem in federated learning (FL). In this work, we identify a cause of unfairness in FL -- conflicting gradients with large differences in the magnitudes. To address this issue, we propose the federated…

Composite federated learning offers a general framework for solving machine learning problems with additional regularization terms. However, existing methods often face significant limitations: many require clients to perform…

In this paper, a new and efficient numerical algorithm by using weak Galerkin (WG) finite element methods is proposed for a type of fourth order problem arising from fluorescence tomography(FT). Fluorescence tomography is an emerging, in…

In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first…

In this article, a nonlinear fractional Cable equation is solved by a two-grid algorithm combined with finite element (FE) method. A temporal second-order fully discrete two-grid FE scheme, in which the spatial direction is approximated by…

The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…

We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…

The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…

We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling…

We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise…

This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…

In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of…

This paper introduces filtered finite difference methods for numerically solving a dispersive evolution equation with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled nonlinear Schr\"odinger…

Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…