Bicubic interpolation can be regarded as a computationally efficient approximation to Lanczos resampling. Uniform manifold approximation and projection (UMAP) is a nonlinear dimensionality reduction technique. These equations are valid within the limits of the paraxial approximation. Often the parametric bootstrap approximation is better than the empirical bootstrap approximation. If formula 69 this is the same as the linear approximation. Classical mechanics is the same extreme high frequency approximation as geometric optics. Calculations are likely to involve rounding errors leading to approximation. The Coulomb approximation is fundamentally an empirical construct. The first computations performed with instantons used the dilute gas approximation. In addition to these more sophisticated models a number of approximation algorithms exist. This allows several results about the hardness of approximation algorithms to be proven. Greedy GQ is a variant of "Q"-learning to use in combination with (linear) function approximation. Geometric optics is often simplified by making the paraxial approximation, or "small angle approximation". Hence, this would result in approximation and statistical errors. The Wigner-Kirkwood series is a semiclassical series with eigenvalues given exactly as for WKB approximation.