It has become quite clear that perception of the "convergence trade" was diametrically backward.
The new time-stepping scheme is composed of two backward Euler steps, but has twice the convergence rate of the backward Euler scheme and alleviates the convergence problems that are often experienced when employing compressive limiter functions.
We analyze the backward-time ancestral process, and prove convergence to a continuous-time coalescent process.
Convergence results for the scheme (i), in the case in which { ρ k } is contained in a compact subset of ( 0, 1 ), can be found in [2]; the convergence analysis of the double backward scheme given by (ii), which can be found in [3] and [4]; the standard convergence analysis for (iii) one can see [5].
The optimal model was chosen as the convergence of the forward and backward models, with consideration of parsimony and plausibility.
Then the state values obtained are used to solve the adjoint equations backward in time; the iterations continue until convergence.
Similarly, the BW update for the probability of transitioning from some state h A to another state h B is The BW algorithm iterates between calculating the forward-backward values and updating the parameters, until convergence.
Structurally, the hierarchy is formed via convergence and divergence of forward and backward connections, while their differential functionality introduces a temporal (and spatial) separation of scales of operation.
For example, Higham and Kloeden proved the strong convergence and its order of the split-step backward Euler (SSBE) method and compensated split-step backward Euler (CSSBE) method for nonlinear jump-diffusion system in [16, 17].
Further we obtain simple finite-dimensional conditions in terms of LMIs for an upper bound T∗ on the minimal time, that guarantees the convergence of the sequence of forward and backward observers on [0,T∗] for the initial state recovering.
