The phrase "approximation to the approximation" is correct and usable in written English.
It can be used in contexts where you are discussing a refined or secondary estimate of an initial approximation.
Example: "In our calculations, we found that the approximation to the approximation provided a more accurate result."
Alternatives: "refinement of the approximation" or "secondary approximation".
Finally, a number of theorems is proven concerning the Plefka expansion, relating the first order mean field and the second order Onsager approximation to the Bethe approximation.
The iterative algorithm has a linear constringent ratio; its solution gives a second-order spatial approximation and first-order temporal approximation to the real solution.
The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations.
We algebraically rank the error of the Chebyshev Polynomial approximation, Taylor's Series approximation and the Gauss-Lanczos approximation to the solution of the SAR model and its variants.
And since the importance density should be chosen to represent a close approximation to the posterior, using a better approximation based on the likelihood, rather than the prior, has been shown to improve performance [13].
In order to obtain a more accurate approximation to the error performance, we propose two more approximations, namely, the geometric approximation and the arithmetic approximation.
We demonstrate that a compound Poisson approximation is an excellent approximation to the exact distribution of occurrence counts.
Differentiation of the piecewise linear approximation yields an approximation to the first time derivative \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{\mathrm {d}}{\mathrm {d}t} v$\end{document}.
First, we show that the Nyström-based eigenfunction approximation is identical to the eigensystem approximation of two matrices.
For example, a Volterra series approximation, analogous to the Taylor series approximation of a function, yields a description of the system based on a series of functionals [49].
