Based on a parametric analysis, we demonstrate the potentials of the proposed method through its comparison with results available from the literature and by means of a convergence study.
By means of the convergence in (3.6), we can deduce the existence of a constant (M>0) independent of k and m such that D_{0}^{ k)}(f,tilde{u}_{0},tilde{u}_{1}, tilde{u}_{0k},tilde {u}_{1k})leq frac{1}{2}M^{2} quad text{for all }m,kin mathbb{N}.
We ran four independent chains under the CAT+GTR+Γ4 model, removing constant sites using the -dc option, as a means of improving convergence as recommended in the PhyloBayes-MPI manual.
We have tested the experiment sixty times, and the numerical results are listed in Table 1, in which 'NC' means the number of convergence; 'ND' means the number of divergence and 'Ratio' means the ratio of succession.
Consequently, timestep sizes can be chosen without stability limitations, which it means higher rates of convergence in comparison with the classical relaxation methods.
That means the order of convergence for time is better than (O tau^{2})), so the numerical result is better than the theoretical result.
We prove that our algorithm converges almost surely to an unbiased estimate of the average of agents' initial states, compute the exponential mean-square rate of convergence, and formally characterize its differential privacy properties.
In this context, IP technology has emerged as a natural means of initiating network convergence and the "All-IP" paradigm has become the implicit assumption for most studies on the next generation architecture design.
Now we derive the strong precompactness property by means of the Vitali convergence theorem.
