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We use our theoretical results to construct schemes which are stable even for very large time steps.
For m = − 2, we find ϵ(t) → − 2 for very large time, and from Equation 15, we get after a long but simple numerical algebra γ ≈ − 1.5.
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Remark 2 If we set γ ∝ τ- x, x > 0, then Equation 7 is reduced for a very large time to its standard form as lim τ → ∞ γ τ → 0 Open image in new window and lim τ → ∞ x > 0 1 1 + γ τ dγ τ dτ = lim τ → ∞ x > 0 - x 1 + τ x 1 τ → 0 Open image in new window.
For very large datasets, the time required for the initial data transfer can be substantial, and will depend on the bandwidth of the cloud provider.
The results obtained through our exact algorithm are presented, and this method shows to be extremely efficient both in obtaining optimal solutions and in computing time for very large instances of the problem at hand.
The processing time for very large images are below 200 ms for backward mapping and below 100 ms for forward mapping for most machines, which is 30 60 times faster than the classical implementation, 5 20 times faster than the FPGA implementation, and up to 6 times faster than other implementations of image rotation.
It is demonstrated empirically that Nanbu's collision operator quite accurately recovers the effects of Coulomb Lorentz pitch-angle collisions, or processes that approximate these (such interspecies Coulomb collisions with very small mass ratio) even for very large values of the collisional time step.
This time for very large structures, can be reduced from months to days.
Heuristic solutions without provable approximation bounds have also been investigated, but computation time for very large networks remains an important issue in these methods as well.
Nevertheless, a limitation of metaMix is the increased processing time for very large datasets.
Consequently, convergence can not be achieved in a reasonable time for very large data files.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com