Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

The object of this paper is a theoretical study of the convergence of approximation methods (Galerkin and finite difference methods) to compute eigenelements of a closed linear operator T in a Banach ...

Dynamical low-rank approximation (DLRA) methods have emerged as a powerful numerical framework for addressing the challenges posed by high-dimensional problems. By restricting the evolution of a ...

This is a preview. Log in through your library . Abstract Practical use of Bayesian methods usually involves obtaining certain characteristics of the posterior distribution of the parameter of ...

Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and ...

Clinical trials have traditionally followed a fixed design, in which patient allocation to treatments is fixed throughout the trial and specified in the protocol. The primary goal of this static ...

In this topic we will advance the fundamental mathematical understanding of artificial neural networks, e.g., through the design and rigorous analysis of stochastic gradient descent methods for their ...

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply ...

Researchers at the University of Illinois Urbana-Champaign have developed a new theoretical framework that could dramatically ...