Approximation theory investigates how complex functions or data can be represented by simpler mathematical entities—such as polynomials, splines, wavelets or ...

Asymptotic expansions of integrals. Regular and singular perturbation methods for ordinary and partial differential equations. Boundary layer theory. Matched asymptotic expansions. Homogenization. Two ...

Asymptotic theory examines the limiting behaviour of probabilistic and statistical quantities as the sample size or problem dimension grows without bound. Key pillars include the law of large numbers, ...

Exact statistics can be useful in situations where the asymptotic assumptions are not met, and so the asymptotic p-values are not close approximations for the true p-values. Standard asymptotic ...