In this talk we present few instances of multilevel approximation methods involving PDEs with random parameters and associated scalar output quantities of interest (QoI). Multilevel methods aim at ...

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 ...

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 ...

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 ...

Peer two-step methods have been successfully applied to initial value problems for stiff and nonstiff ordinary differential equations (ODEs) both on parallel and sequential computers. Their essential ...

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 ...

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 ...

In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea ...

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 ...