Sentence examples for matrices required in from inspiring English sources

In order to avoid the formation of blocking matrices required in the original algorithm, Zoltowski et al. proposed a data level recursive MSNWF algorithm [23, 24] as shown in Fig. 2, which effectively reduces the computational complexity.

A new approach based on the single value decomposition technique has been developed to derive the compatibility matrix required in the force method.

Furthermore, the paper specifies the input covariance matrix required in order to attain the capacity.

The most significant matrix during linearization is matrix A. This matrix is required in order to determine the eigenvalues.

(2006) go on to derive tests, based on the distribution of quadratic forms, for the presence of one or more discontinuity along the curve, and these methods adapt directly to the case of derivative estimation, with only a change in the weight matrices required.

Actually, we chose different GS models for RRGS_HYB and RRGS_PAR for computational reasons: two G matrices were required in the model chosen for RRGS_PAR.

It is noted that the matrix G[ s i ] is of dimension N×N L, and the matrix B z ≜ I L ⊗ B is of dimension N L×(Q+1 L; the (Q+1 L×(Q+1)L matrix inversion required in (56) and (57) is 1 N R of that needed in (51) and (52) and therefore only 1 N R N T of that needed in (17) and (18).

It is noted that the matrix Φ[ s i ] is of dimension N R N×N R N L, and the matrix ( I N R L ⊗ B ) is of dimension N R N L×N R (Q+1 L; the N R (Q+1 L×N R (Q+1 L matrix inversion required in (51) and (52) is only 1 N T of that needed in (17) and (18).

To search for the optimum b p and m values, the total number of matrix inversions required in [31] is (P + K - 1 Imax, where PImax iterations are required to determine b p, while (K - 1 Imax iterations are required to determine m.

A weight matrix is required in the calculation of Moran's I values, so that regions close to each other are given a greater weight than those located further apart; the weights were defined as 1/ d, where d represents the straight line distance between the mid-points of two regions.

The model (9) then generates the same variance model as (4) and the predicted random effects for the original model can be recovered from those found using (9) as a ˜ = (I t ⊗ P T (P P T ) − 1 / 2 ) a ˜ * with variance matrix var (a ˜ ) = (I t ⊗ P T (P P T ) − 1 / 2 var (a ˜ * ) (I t ⊗ P P T ) − 1 / 2 P and only diagonal elements of this matrix are required in computing the outlier statistics (7).