In practice this can be avoided by a coarse-to-fine multiscale scheme.

Numerical Analysis Numerical Analysis

While the asymptotic distribution of the rescaled estimation error can be derived by relatively standard arguments, the convergence of the pattern does not simply follow from the convergence in distribution, and requires a careful and separate treatment.

Statistics Theory Statistics Theory

In addition to these capabilities, the active strategy can also hide sources of particles, at the cost of prior knowledge of the expected net particle charges in the reference graph.

Probability Numerical Analysis Numerical Analysis 05C81, 31C20, 65M80, 31B10

The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to reproduce the finite element approximation.

Numerical Analysis Numerical Analysis

We prove an Andr\'e--Oort-type result for a family of hypersurfaces in $\mathbb{C}^n$ that is both uniform and effective.

Number Theory 11G18, 14G35

Given a nonlinear matrix-valued function $F(\lambda)$ and approximate eigenpairs $(\lambda_i, v_i)$, we discuss how to determine the smallest perturbation $\delta F$ such that $[F + \delta F](\lambda_i) v_i = 0$; we call the distance between the $F$ and $F + \delta F$ the backward error for this set of approximate eigenpairs.

Numerical Analysis Numerical Analysis 65H17, 65F15, 15A18

This paper analyzes the estimation of econometric models by penalizing the sum of squares of the residuals with a factor that makes the model estimates approximate those that would be obtained when considering the possible simple regressions between the dependent variable of the econometric model and each of its independent variables.

Statistics Theory Statistics Theory 62J05

This paper presents the Logic-based Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP problems involving ordered Boolean variables.

Optimization and Control

Randomized iterative methods, such as the Kaczmarz method and its variants, have gained growing attention due to their simplicity and efficiency in solving large-scale linear systems.

Numerical Analysis Numerical Analysis

In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations.

Number Theory