Since the resultant sparse approximation involves nondifferentiable functions, locally competitive algorithm and forward Euler discretization method are exploited to approximate the nonsmooth objective function, yielding a smooth optimization problem. Alternating direction method of multipliers is then applied as ...
16.5.1.3.1 Forward Euler method Forward Euler is the simplest numerical integrator. Using forward Euler integration, Eq. (16.78) writes (16.79)xt+1=xt+ftΔt where xt = x(t), xt+1 = x(t + Δt), and ft = f(xt, t). Eq. (16.79) is just an evaluation because it has an exp...
Discretize (1) using a forward-Euler scheme with sampling period (2)Δ=1 and find the transfer function between u(k) and y(k) Homework Equations The Euler method is yn+1=yn+hf(xn,yn) The Attempt at a Solution Laplace transform of (1) yields s3Y(s)−s2Y(s)=U(s) From my teac...
Generally speaking the accuracy of the system employing the midpoint Euler method is higher, but as the inputs are only known at the current moment, a mixture of the forward Euler method and midpoint Euler method is used for the above Eq. (14), so that \(X(\xi )=\left( {X(t)+...
The worst methods are Arbitrage-free discretization A A: Terminal Log(S(n)) B: Terminal Y[n] C: Spot Log(S[n]) D: Spot R[n] B 63 D C Fig. 12. Swaption pricing 0 2 4 6 8 10 Caplet Expiration (in years) the straightforward Euler discretizations of Sn and log Sn . The best...
First of all, motivated by the local property of jump diffusion processes, the Euler method is used to solve the associated forward stochastic differential equation with jump, which reduce dramatically the entire computational complexity, however, the quantities of interests in the backward stochastic ...
method;dual-timesteppingmethod 相对于 uler 方程而言 , avier-Stokes 方程 更精确地描述了流体的流动 , 对于绕前飞旋翼的 流动就更是如此 只有 avier-Stokes 方程才能准 确地描述涡的形成和输运 ; 在前飞过程中 , 相对 速度较小的后退桨叶为了获得较大的升力 , 其工 作迎角较大 , 导致绕后退桨叶的流动出...
Due to the Eulerian discretization error, the objective 𝑔(𝑋𝑇)g(XT) cannot be reached exactly, and the loss function cannot go exactly to zero. If the neural network’s output is permitted to depend not just on the variable realizations at moment t, but also on the long-term and...
Stability and Hopf Bifurcation Analysis on a Numerical Discretization of the Distributed Delay Equation A kind of discrete logistic model with distributed delays obtained by the Euler method is investigated, where t...
When the right-hand side in the differential inclusion is a compact-valued, Lipschitz continuous setvalued function it is shown that the convergence in Hausdorff distance of reachable sets for a forward Euler discretization is linear in the time step....