Sentence examples for necessary matrix from inspiring English sources
An analytical method, based on the rigid finite element method, for calculating the necessary matrix of rotor receptances expressed in a rotating system of co-ordinates is given.
On the other hand, due to the Toeplitz structure of the (R_{u_{t}}) matrix, one can resort to a Levinson-Durbin type technique [42] to recursively compute the necessary matrix product operations.
In this paper, we present a new boundary integral equation approach, valid for both interior and exterior problems, which requires the solution of a single linear system of dimension N + M. We solve this system by making use of an iterative method (GMRES) combined with the fast multipole method for the rapid calculation of the necessary matrix vector products.
The advantage of this modification is that the symmetry reduces the number of necessary matrix memory accesses by approx. 50% (Golub and Van Loan, 2013, p.18).
The digestion followed by sample dilution and, if necessary, matrix evaporation, showed analyte recoveries of 103 ± 5% for As, 95 ± 11% for P, 107 ± 6% for Cd, and 100 ± 8% for Cu (STD, n = 21).
The free vibration of loaded beams is formulated in a compact matrix form and all necessary matrices are explicitly given.
One problem associated with ETD schemes is the accurate calculation of the necessary matrices; we implement and discuss in detail a variety of different methods including direct computation, contour integration, spectral expansions and recurrence relations.
It was hypothesised that the former would trigger necessary matrix-metalloproteinase (MMP) expression and the latter not [ 7].
Similarly, Aktuğ (2012) derived a necessary specificTykhonov matrix to estimate the datum transformation parameters from a set of distorted terrestrial network coordinates.
Through qRT-PCR analysis, we found significantly increased expression of elastin, fibronectin, and collagen I, indicating the synthesis of necessary extracellular matrix components.
In this study, the concept of an ideal distribution of the velocity vectors is introduced, the necessary Tykhonov matrix was derived analytically, and the multicollinearity between Euler parameters was handled with regularization.
