Sentence examples for computing the gradient from inspiring English sources

Moreover, it is shown that computing the gradient of the cost function analytically provides significant savings in computer runtime over finite-difference approximations.

In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters.

It is found that the error in modulus obtained by directly computing the gradient of stress strain curve is relatively small and can be used in analysis.

Isotropy of the solution is obtained when the directional derivatives method, specific for each lattice, is applied for computing the gradient terms.

The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities.

At each conjugate-gradient iteration, it is only involved with computing the gradient of objective function.

According to the characteristics of the Cartesian grids, the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces, which can significantly improve the solution converging speed.

The application of the same LMS algorithm by alternatively computing the gradients with respect to and results in the following update equations: (32).

The computational efforts are greatly reduced by introducing a meta-model (e.g. a response surface), using an advanced simulation method for the reliability analysis and an efficient algorithm for computing the gradients of the failure probabilities.

Since the AFD and the proposed algorithm use the same matrix inverse operations, which consist of the most significant part of the computation, to compute the gradient of the objective values, both algorithms have similar computational complexity O(m 3) in each of the iterations (refer to [28]).

The proposed procedure computes the gradient of a cost function by computational costs comparable to a model simulation itself, thus enabling the management of large-scale systems.