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Taking the l1 norm error of 27 for example, the iteration times of our new algorithm is about 200.
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The model results for thermal efficiency are within ± 5% for 59 of the 63 designs and have an L2 norm error of 3.0%.
By using the Nietzsche technique and Theorem 7, we easily obtain the following (L^{2}_{omega}) norm error estimates.
The computed errors are defined by l 2 norm error: E ( f ) = 1 n ∑ i = 1 n ( f ( x i ) − f r ( x i ) ) 2, (4.6).
Tables 1 and 2 present, respectively, the absolute error and the (L^2) norm error for (u x,t -{widetilde{u}}(x,t -{widetilde{u}nt values of q.
The temporal rate of convergence of (L_{2}) norm error as a function of the time step (Delta t) for (alpha = 1.75) is shown in Fig. 6.
Under the same conditions of Theorem 6, when (Delta t=O(N^{-1})), the (L^{2}_{omega}) norm error estimates between the solution for Problem 3 and the series of solutions of Problem 5 are as follows: biglVert u(t_{n} -u_{N}^{n} bigrVert_{n} -u_{a} = O bigl(Delta t^{2},N}^{n} bigrVertuad1leq nleq K, 2leq qleq N+1.
Fixing the spatial step (h=1/1text000) and taking different temporal steps, Table 1 presents the maximum (L_{2}) norm errors and convergence orders of our schemes; fixing the temporal step (tau =1/10text000) and taking different spatial steps, Table 2 presents the (L_{2}) norm errors and convergence orders in spatial direction.
We also present a generalization of the H2-norm error formula to any projection of dynamics method.
We derive a discrete version of Antoulas's H2-norm error formula and show how to adapt it to some special cases.
The linear reconstruction measure (LRM), which determines the nearest neighbors of the query sample in all known training samples by sorting the minimum L2-norm error linear reconstruction coefficients, is introduced in this paper.
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