In addition, we show how to incorporate knowledge of the traffic load, and we devise approximation algorithms to control the sleep/wake-up cycling to provide maximum energy conservation while discovering enough communication opportunities to handle that load.
The constrained path approximation is used to control the sign problem.
Assume now that the time instant t is arbitrary, i.e., we want to approximate e tA v for some t > 0. In order to control the approximation error, we calculate e tA v stepwise by exploiting that for τ1, τ 2 ≥ 0. For a step size τ, we approximate e τA v by || v ||2 because the Krylov subspaces associated with A and τA are identical and.
It is possible to control the approximation error at each step by estimating the difference between approximations at order N − 1 and N. By wisely choosing the coefficients a i j and c i, intermediate points calculated in the method can be used to calculate two separate evaluations of the solution: A first evaluation ψ n + 1 = ψ n + Δ t ∑ i = 1 N b i k i accurate at order N.
The first technique is to handle constraints on control variables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at element knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies.
The derivation of the residual-based error estimator η (T, ⋅ ) follows similarly to the homogeneous case and differs only by adding an oscillation term to control the approximation of the Dirichlet data [38,39,109,110].
Thus, the ETJEM permits a much wider choice of polynomial bases to control the error of approximation than the traditional evidence-theory-based orthogonal polynomial approximation method, in which only the Legendre polynomial is used for approximation.
However, as the regression model is used to control the degree of approximation, the loss in diversity between the two methods is within 2%.
The first step is to derive a posteriori error estimates for the approximation to the control variable.
A highly accurate approximation to the control law is found in closed form.
