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For good approximation,, so (12).
The authors propose a simple estimate of the width in the Gaussian kernel for good approximation.
We further showed that the algorithm learns meaningful dictionaries on corrupted image data and demonstrated the importance of considering the presence of a low-rank component for good approximation properties of the dictionary.
We assume that there are two important factors for successful SAO: one is parameter adjustment for good approximation, and the other is to find the unexplored regions for global approximation.
First, we compute the cosines of principal angles, between the exact and the approximate eigenvectors: cos Angle = u i 2 + u ̃ i 2 - u i - u ̃ i 2 u i 2 u ̃ i 2, i = 1,..l, which should be close to 1 for good approximation.
Similar(55)
Note, however, that if the probability (Phi _{g,mathbb {P}}(B)) is small which is, e.g., the case if B is a "thin" set or has large distance from the center of the distribution (Phi _{g,mathbb {P}}) then relatively large sample sizes are needed for good approximations via simulation.
Given the results from the simulation data, we encourage the reader to use this script and check whether the formulae presented in the paper will provide for a good approximation of Z0 for his/hers particular multinomial distribution.
For a good approximation of the error using (3), and for computational simplicity, the decision region was chosen as an -dimensional hypersphere centered at and with radius, where and are the parameters to be optimized [5].
In fact, Bh≥4 bits is enough for a good approximation.
Most of the works developed within this model deal with independent MT for which good approximation algorithms have been designed.
We propose a solution method that involves a finite number of constraints, and identify the number of samples sufficient for a good approximation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com