Sentence examples for higher order matrix from inspiring English sources

In this paper, we study an efficient strategy for constructing preconditioners for the Newton Krylov matrix-free methods without forming explicitly the higher order matrix associated with each linear step in the Newton iteration.

However, the polynomial method needs to calculate the high order matrix multiplication, therefore, it can not be implemented easily.

This relieves the load of an on-line updated calculation of the channel coefficients which includes the inversion of a high order matrix.

Based on either a high-order matrix polynomial model or a first-order state-space model, this paper emphasizes the comparison of numerical conditioning and stability, as well as the modal parameter estimation, among EMA methods.

In addition, we show that EVD can be extended to the high-order matrices.

The desired higher order mass matrix is then deduced from the mixed mass matrix by optimizing the linear combination parameter to achieve the most favorable order of accuracy.

For the 1D Euler Bernoulli beam problem, it is shown that a new higher order mass matrix can be directly established by optimizing a reduced bandwidth mass matrix.

Consequently a particular higher order mass matrix can always be set up for a superconvergent computation of arbitrary vibration frequency.

It is proved that the optimal combination parameter for higher order mass matrix depends on the wave propagation angle.

A generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices.

As a result, 4th and 6th orders of accuracy are observed for the proposed quadratic and cubic higher order mass matrices, while their corresponding consistent mass matrices are 2nd and 4th order accurate, respectively.