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For the rank-ℓ approximation, ε is zero or P= P. Consequently, adding more singular values and their corresponding singular vectors reduces the approximation error.
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By using neural network, the unknown nonlinear function is approximated and a robustifying term is used to reduce the approximation error and compensate the effect of external disturbance.
Using this formulation, the gradient information on each data point can be used to significantly reduce the approximation error.
The high-fidelity reactor physics calculation attracts a lot of attention because of the development of high performance computing technology and increasing requirement of reducing the approximation of traditional methods.
For example, we reduce the approximation ratio for the connected facility location problem from 8.55 to 4.00 and for the single-sink rent-or-buy problem from 3.55 to 2.92.
We also prove that, the Galerkin approximation for the residual Hamiltonian can reduce the approximation error to O εk/2), where k depends on the number of Hagedorn wave packets added to the dynamics.
Moreover, if (e^v) can be reduced, the approximation of optimality may also be improved.
In order to further reduce the approximation error of the synthesizer circuit, it is possible to increase the order of approximation.
Since there are more choices for the psychological threshold of a factor, Rule 3 is introduced to fully utilize the information from the answer sheets and to reduce the approximation error.
Consequently, it does not converge to the CWR when reducing the approximation, while scrm does (Fig. 2).
Additionally, under RHH models in which variation is strongly reduced, the approximations of Kaplan et al. (1989) and Stephan et al. (1992) are violated, owing to overlapping sweep patterns (Przeworski 2002).
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