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 ...

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 ...

A firm that wants to use a large language model (LLM) to summarize sales reports or triage customer inquiries can choose between hundreds of unique LLMs with dozens of model variations, each with ...

The Bjerksund-Stensland model is a key method for pricing American options. It helps investors determine optimal times for exercising options with dividends considered.

SIAM Journal on Applied Mathematics, Vol. 50, No. 6 (Dec., 1990), pp. 1517-1532 (16 pages) An approximation method of Moore for Kelvin-Helmotz instability is formulated as a general method for ...

This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational ...

The travelling salesman problem (TSP) remains one of the most challenging NP‐hard problems in combinatorial optimisation, with significant implications for logistics, network design and route planning ...

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 ...

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 ...

An important part of the marginal maximum likelihood method described previously is the computation of the integral over the random effects. The default method in PROC NLMIXED for computing this ...