Sentence examples for order of basis from inspiring English sources

Then, we also perform the re-ordering procedure to correct the mixed order of basis vectors caused by the initial sorting and obtain a re-ordered reduced matrix H'in,αas follows: H ′ in, α = h ′ α, 1, h ′ α, 2, h ′ α, 3, h ′ α, 4 where h ′ α, θ ( i ) = u i. (20).

Therefore, the order of basis vectors is changed, when swapping event occurs.

But due to the construction way of local approximants, it is time consuming and difficult to change the order of basis function.

Let π be the permutation order of basis vectors caused by the swapping event, so that we can express s'π (i)= g i, where s'(i is the reduced basis of s'.

Let θ be the permutation order of basis vectors, then the input matrix Hin, αof OLR-block is sorted as follows: θ ( i ) = arg min j ≠ θ ( k ) k < i h α, j. (17).

Moreover, arbitrary high order degree of basis functions can be used and their regularity enables the use of a low number of elements.

For the physically accurate mode, it is shown analytically that the numerical dispersion relation is accurate to order 2p+2, where p is the highest order of the basis polynomials.

It is found that for any given order of the basis functions, there are at most two spatially propagating numerical wave modes for each physical wave of the partial differential equations (PDE).

From the comparison of error norms and convergence rates for NURBS and discretisations based on Lagrangian polynomials, smaller errors and similar convergence rates are found for the proposed method for the same polynomial order of the basis functions and a comparable mesh size.

A representative image of the order of the basis functions is shown in Fig. 2(a).

The order of each basis function was m, and we used cubic-splines, that is, m = 3, as in EPP.