Related papers: A Numerical-based Parametric Error Analysis Method…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
We propose a framework for the derivation and evaluation of distributed iterative algorithms for receiver cooperation in interference-limited wireless systems. Our approach views the processing within and collaboration between receivers as…
We study the time-sliced thawed Gaussian propagation method, which was recently proposed for solving the time-dependent Schr\"odinger equation. We introduce a triplet of quadrature-based analysis, synthesis and re-initialization operators…
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…
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing…
We consider the problem of accurate computation of the finite difference $f(\x+\s)-f(\x)$ when $\Vert\s\Vert$ is very small. Direct evaluation of this difference in floating point arithmetic succumbs to cancellation error and yields 0 when…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally…
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
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…
This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error analysis that explains the propagation of errors in the…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
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…