Sentence examples for approximation limits from inspiring English sources
This approximation limits the range of application of the solution to small ambient gradients or relatively high frequencies.
Later on, Becke introduced the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid approach that can overcome the HF approximation limits [19, 24 26].
As can be observed qualitatively in Fig. 5 b, PPCA's rotation approximation limits its result to getting better rotation estimate in frame 50.
Based on the descriptions for the velocity potential of the incident beam and the scattering coefficients of the sphere in the long-wavelength approximation limit, simplified expressions for the spin and orbital radiation torque components are derived.
Further, also the choice of the defocus steps affects the accuracy of the phase reconstruction, as the intensity derivative is an approximation limited by noise (small defocus steps) and artifacts due to non-linearity (large defocus steps).
Therefore, we use the theoretical error probability approximation, limited to the nearest neighbors as in [25]: considering an impact of the received constellation, the error only comes from the choice of one neighbor at the distance dmin.
This experimental setup allows us to test our algorithm to recover realistic tubular structures accurately even when highly absorbing areas, exceeding the Born approximation limit, are present in the medium [ 8, 25].
To simplify the nonlinear terms and to conserve the total mass and total angular momentum to round-off accuracy, we introduce a "stratified" approximation which limits the nonlinearity of the equations to quadratic.
The experiments described in the preceding discussion involve finite sample spaces for the most part, although the central limit theorem and the Poisson approximation involve limiting operations and hence lead to integrals and infinite series.
For special transmission functions such as Fresnel lenses, approximations can be found analytically16,17, but these methods do not generalize to arbitrary target transmission functions, and the accuracy of the approximation is limited.
