Sentence examples for by finite difference approximation from inspiring English sources
DFE-WF, Θ∗, for every sample of the channel is obtained by running a gradient descent type of algorithm on the cost function (4) itself, where the gradient was approximated at each point by finite difference approximation, [EΘ + Δ(X t −s]2−E Θ (X t −s)2) /|Δ|.
Treatment initial boundary value problem for parabolic PDE by finite difference approximation has many difficulties for accuracy and complexity.
A theoretical model of the cable with multi-degree-of-freedom is first obtained through discretization of the partial differential equations by finite difference approximation.
However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem.
That is, when the gradient of the objective function is calculated by finite difference approximation, the algorithm tends to use nearby points, which can even violate the given constraints.
In addition, when the derivatives are not available or are extremely expensive to compute, we approximate them by finite difference approximations having the desired accuracy to derive a new class of discrete quasi-interpolants.
The angles α t i and curvatures κ t i are reconstructed from the fiber points η t i by finite difference approximations.
Typically, a gradient-based optimization problem is solved more accurately and with higher efficiency when analytical gradients are provided compared to numerical gradients, which are calculated by finite-difference approximation.
Rashidinia and Mohammadi [33] developed an approximation for finding the numerical solution of differential equation (3) by replacing the time derivative by a finite difference approximation and the space derivative by sextic spline functions using off-step points to obtain three-level implicit methods of accuracies (O k^{2}+h^{4})) and (O k^{4}+h^{4})).
Radial smoothing, i.e. regularization across layer boundaries, is applied by a finite difference approximation of the vertical gradient (acting on the respective spherical harmonic coefficients).
The flow field is discretized by a conservative finite difference approximation on a stationary grid, and the interface is explicitly represented by a separate, unstructured grid that moves through the stationary grid.
