Sentence examples for present approximation from inspiring English sources

For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost, both double exponential in the POMDP state space size; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives.

We present approximation algorithms for this optimization problem.

In this paper we present approximation algorithms for the two dimensional strip packing problem with unloading constraints.

We observe that the present approximation is agreed with numerical solution, and the maximum relative error of present solution is less than −3% in Figure 4.

The present approximation agrees with numerical solution, and the maximum relative error of present solution is less than −3% in Figure 8.

Compared with the finite element method, two examples in power law diffusivity and van Genuchten model are shown to test the accuracy of present approximation.

Dotted lines show the present approximations, and solid lines show the results by the FEM. Figure 8 Relative errors of present approximations and the FEM.

The dotted lines show the present approximations, and solid lines show the results by the FEM as time increases.

Dotted lines show the present approximations, and solid lines show the results by the FEM. Figure 4 Relative errors of present solutions and the FEM.

By the comparison of the results obtained using the presented method in Table 2 with the RKM, it is easily found that the present approximations are more efficient.

We also present approximations for the Kullback-Leibler divergence between GMMs, which have not been previously used in audio similarity measurement.