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This contribution introduces a novel signal extrapolation algorithm and its application to image error concealment. The signal extrapolation is carried out by iteratively generating a model of the signal suffering from distortion. Thereby,…
In this paper, we develop an EXCMG method to solve the three-dimensional Poisson equation on rectangular domains by using the compact finite difference (FD) method with unequal meshsizes in different coordinate directions. The resulting…
In this paper, the Newton-Anderson method, which results from applying an extrapolation technique known as Anderson acceleration to Newton's method, is shown both analytically and numerically to provide superlinear convergence to non-simple…
We present two approaches for enhancing the accuracy of second order finite difference approximations of two-dimensional semilinear parabolic systems. These are the fourth order compact difference scheme and the fourth order scheme based on…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space,…
This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main difficulty lies in handling the interaction between the…
The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
The main goal of this paper is to analyze a family of "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here a first step toward a rigorous…
In this paper, we treat the problem of evaluating the asymptotic error in a numerical integration scheme as one with inherent uncertainty. Adding to the growing field of probabilistic numerics, we show that Gaussian process regression (GPR)…
Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by matrix structures, property of eigen-solutions, size of…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and…
In \cite{wang2023towards}, a dual-consistent dual-weighted residual-based $h$-adaptive method has been proposed based on a Newton-GMG framework, towards the accurate calculation of a given quantity of interest from Euler equations. The…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…