Sentence examples for behavior of the approximation from inspiring English sources
We predict the error behavior of the approximation and demonstrate this on an application.
We prove that the behavior of the approximation numbers of the finite sections Tn(a)="PnT a Pn depends heavily on the Fredholm properties of the operators T(a) and T(˜a)(a˜(t)="a(1/t)).
However, using this method to approximate the distribution of the SCN requires normalization and the behavior of this approximation could be affected especially at high SNR.
The selection of the knots in B-spline approximation has an important and considerable effect on the behavior of the final approximation.
Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS.
Therefore, we may be able to infer properties of the behavior of paths of the solution from the path behavior of the Galerkin approximations.
We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of "coarse limit cycles" of the macroscopic behavior, and the approximation of their stability through estimates of the leading "coarse Floquet multipliers".
The well-posedness and long-time behavior of the modified Boussinesq approximation equation can be referred to [7].
Figure 1 Asymptotic behavior of the backward Euler approximation with different initial step size Δ 0, left: Δ 0 = 0.1 ; right: Δ 0 = 1.
The left one of Figure 1 describes the mean square asymptotic behavior of the backward Euler approximation E | Y n | 2 of Eq. (39) with initial step size Δ 0 = 0.1 ; the right one of Figure 1 describes the mean square asymptotic behavior of the backward Euler approximation E | Y n | 2 of Eq. (39) with initial step size Δ 0 = 1.
As a basic tool, we use an analog of approximate Bernstein and Jackson inequalities and an abstract quasi-normed Besov-type interpolation space B p, τ α ( A ), associated with exponential type entire vectors of A, which sharply characterizes the behavior of the best spectral approximation.
