Sentence examples for remarkable approximation from inspiring English sources

The effective multi-objective strategies including the fast non-dominated sorting and the farthest-candidate selection are developed for saving and retrieving the Pareto optimal solutions with remarkable approximation as well as uniform spread of Pareto-optimal solutions.

BPNN is a widely used machine learning technique for classification due to its remarkable function approximation ability.

He also obtained a remarkable rational approximation 355 / 113, which yields π correct to six decimal digits.

The Normal distribution is strictly only the limiting form of the sampling distribution as the sample size increases to infinity, but it provides a remarkable good approximation to the sampling distribution even when the sample size is small and the distribution of the data is far from Normal [Page 94, [ 29]].

She'll cut down jumpers to make leggings, wear big jumpers with knitted mini skirts and thick tights - a remarkable and instinctive approximation of the Joseph Tricot look, in fact.

It is remarkable that our approximation of natural motion by the rigid translation of natural images revealed substantial utility for higher-order correlations in motion processing.

Examples considered in the paper illustrate a remarkable accuracy of the approximation in comparison with exact integration.

It turns out that this approximation shows remarkable similarities to the AIC: \[ \text{BIC}[M] \; = \; - 2 \log P(s \mid h_{\hat{\theta}(s)}) + d \log n. \] Here $\hat{\theta}(s)$ is again the maximum likelihood estimate of the model, $d = dim(M $ the number of independent parameters, and $n$ is the number of data points in the sample.

The approximation is remarkable in that simultaneously: (i) it has an extremely simple final form; (ii) in situations for which it is designed it is typically much more accurate than is the large sample normal approximation; and (iii) it is able to capture most of those stylized facts that characterize lack of identification and weak instrument scenarios.

The exact mathematical description of these approximations gives remarkable generalizations of the central limit theorem from sequences of random variables to sequences of random functions.

Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.