This approximation is tractable if {Λ n (y)} can be evaluated efficiently [25].
The comparison with Monte-Carlo simulations demonstrates that the statistics can be evaluated efficiently and precisely.
Each part can then be evaluated efficiently with appropriate fast transform algorithms.
Alternatively, since the integral is a convolution, it can be evaluated efficiently using the fast Fourier transform and multiplication in frequency space.
The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equations (DAEs), and the time dependent potentials are evaluated efficiently using fast convolution algorithms.
Through simulating and analyzing the distribution of the flushing flow's total pressure, the flow speed at the toilet-basin surface and the siphoning bent tube, the toilet performance can be evaluated efficiently and conveniently.
The advantages of the criterion include the fact that it can be evaluated efficiently and exactly, without asymptotic approximations, and importantly, there are no adjustable hyper-parameters, which makes it applicable to both small and large amounts of data.
As the graph-distance for a pair of nucleotides in a given secondary structure can be computed in O(n log n) time by Dijkstra's algorithm with Fibonacci heap [ 19], even large samples can be evaluated efficiently.
It turns out, however, that the HF contribution cannot be evaluated efficiently for plane-wave basis sets and increases computation times by an order of magnitude, and calculations on crystal structures with hybrid functionals are still rare.
In this study, an improvement in condition of the patients was evaluated more efficiently with RNFS system by highlighting even the slightest improvement.
