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The experience of applying such algorithms is to first use the conjugate gradient method to get a close solution and then use Newton's method to achieve the solution within machine accuracy.
That is, the continuous system possesses a good characteristic that its solutions converge asymptotically to an equilibrium if the given inverse problem is consistent; otherwise, a close solution to the complete solution can be found [35].
As shown in Eq. (4) and (5), the L2 norm sparse constraint objective function has a close solution x i =P i y i, where projection matrix is precomputed offline by a set of low- and high-image patch pairs.
Since x i is the close solution with image sparse prior constraint, we transfer the matrix weights to one convolution layer that will make our network have an inherent attribute to take image sparse prior into account and the output x i will be a more accurate high-frequency prediction.
The close solution to Equation (3) is (4) m ˜ = 1 − α I − α M ― − 1 m Similarly, graph Laplacian scores can be derived to measure the relevance between the phenotypes and the target phenotype p with the close solution (5) p ˜ = 1 − β I − β P − − 1 p where P ¯ is the normalized P and parameter β ∈ (0, 1).
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Fig. 4 Closed solution versus exact.
And the radius is the distance between the center and another closest solution.
Let (v_{k}in C^) be the closest solution to (x_{k}).
Also, Eq. (16) explains that RAS result is closest solution from the original matrix.
Therefore, the direct linear transformation (DLT) [29] is proposed to achieve a closer solution to the ideal Q.
where d i is the Euclidean distance between solutions i and the closest solution to it in the Pareto sets of solutions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com