Sentence examples for order of summation from inspiring English sources

We describe an algorithm that computes a reproducible sum of floating point numbers, independent of the order of summation.

We show that such convergence is partially insensitive to the order of summation of the expansion.

Specifically, here is then the synthesis equation for the Fourier transform if we substitute this definition for the Fourier transform of the periodic signal into this expression then when we do the appropriate bookkeeping and interchange the order of summation and integration the impulse integrates out to the exponential factor that we want.

Thus, interchanging the order of summation has no effect.

If we interchange the order of summation, we reach (61).

Then, by interchanging the order of summation, we obtain the following (2.4).

Now, formally the convolution property can be developed by taking the convolution sum, applying the Fourier transform sum to it, doing the appropriate substitution of variables, interchanging order of summations, et cetera, and all the algebra works out to show that it's a product.

Hence, we can interchange the order of summations in (44).

Its proof is straightforward and can be achieved directly by changing the order of summations.

Consequently, the series in (28) is absolutely convergent, and we can interchange the order of summations in (25).

The following inequalities could be deduced by using Young's inequality and norm inequalities with the help of changing the order of summations or exchanging the indices of the summations: (58).