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These collocation coefficients can be efficiently computed using the fast Fourier transform (FFT).

These quantities can be efficiently computed using fast algorithms for partitioning a graph into its communities and for identifying a graph's kmax-shell [39].

Note for example in Equation 24, the matrix inversion is calculated on diagonal matrices; the parameter N is a power of 2 then the IFFT can be efficiently computed using the radix-2 FFT algorithm.

One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed.

Equation 7 can be efficiently computed using Dynamic Programming (DP), as summarized by Algorithm 1 below.

When interpreting distance fields as level sets, they may be efficiently computed using level set methods like Fast Marching [23].

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The values of are efficiently computed using the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm [36].

To this end, the objective function is the expected value of a scalar function of the Fisher information matrix, which is efficiently computed using the sigma point method.

The nodes and weights can be efficiently computed by using the approach proposed in [33].

Note that the values of ( 2{widehat{omega}}_{dp} ) and ( {widehat{omega}}_p ) can be obtained as the location of the dominant peak of the magnitude squared of the Fourier transform ( {left|mathbf{b}left({omega}_{dp}right){mathbf{y}}_p^2right|}^2 ) and |a H (ω p )Ŝ*Y p |2, which can be efficiently computed by using the FFT with vectors ( {mathbf{y}}_p^2 ) and Ŝ*Y p padded with zeros, respectively.

The eigenvalue-function pair of the 3D Schrödinger equation can be efficiently computed by use of high order, imaginary time propagators.

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