The phrase "approximation has been applied" is correct and usable in written English.
It can be used in contexts where a method or technique has been used to estimate or simplify a value or result.
Example: "In this study, an approximation has been applied to the data to facilitate analysis and interpretation."
Alternatives: "an estimate has been utilized" or "a simplification has been employed."
This is expected, since a 1st-order Taylor approximation has been applied (9) in the computation of the quantization noise.
Tsunami propagation has been simulated by long-wave (non-dispersive) equations, and this approximation has been applied to model observed tsunamis especially in near fields (e.g., Aida, 1969; Satake, 1985; Tsushima et al., 2011).
The linear approximation has been applied in nonlinear regression analyses [ 18].
In a previous work (Ciarletta and Ben Amar 2012), WKB approximation has been applied to the circular geometry and was demonstrated with good accuracy of the approximated dispersion relation with respect to the existing numerical results in biomechanics literature (Moulton and Goriely 2011).
Dynamic Monte Carlo simulations with the binary collision approximation have been applied to the synthesis of DLC films by PBII.
Dynamic-Monte Carlo simulations with the binary collision approximation have been applied to the synthesis of DLC films by ion beam-assisted deposition.
Landau Zener and Rosen Zener approximations have been applied for the calculation of rate coefficients of electron energy transfer processes in collisions of two molecules.
This class of nonlinear Yosida approximations have been applied to approximation solvability of nonlinear inhomogeneous evolution inclusions of the form f ( t ) ∈ u ′ ( t ) + M u ( t ) - ω u ( t ), u ( 0 ) = u 0. for almost all t ∈ [0, T], where T ∈ (0,1) is fixed, ω ∈ R (see [1]).
The effective medium approximation (EMA) has been applied to a flow through a porous medium filled with fibrous collectors for the prediction of permeability and the removal (or filtration) rate of colloidal particles.
Thus, the nonlinear Full Approximation Scheme (FAS) multigrid method has been applied to solve this system of algebraic equations, which has been shown the nearly optimal complexity numerically.
The approximation capability of artificial neural networks has been applied to the midcourse guidance problem to overcome the difficulty of deriving an on-board guidance algorithm based on optimal control theory.
