Sentence examples for matrices we replace from inspiring English sources

In case of square matrices we replace M n, n by M n.

To further reduce the computational costs of the MS preconditioning matrix, we replace the real Toeplitz matrix T involved in T̃ by a circulant matrix, obtaining a preconditioner for the discretized linear system from the space fractional coupled nonlinear Schrödinger equations.

Then, we replace matrices M i given by (24) into (19); together with the admissible filter parameter, matrices are defined in (25) and (26).

We replace each matrices in (17) as a substitute to to generate commuting matrices.

If we replace the matrix A in Theorem 2.1 by identity matrix, then we immediately get the following result which is due to Erkuş and Duman [8]: Corollay 2.2.

By matrix completion method [ 28– 30], we replace solving low-rank problem with dealing with nuclear norm [ 31]; then problem (7) can be rerepresented as (8) min ⁡ Z   || Z || ∗,   s.

Furthermore, we replace the Toeplitz matrix T by an appropriate circulant matrix C and obtain the preconditioned MS (PMS) iteration method.

In this paper, we present an implementation that uses the analytical solutions of these transition matrices to replace the numerical calculations.

We can conclude that while generating DFT commuting matrices, a good choice is to chose real, symmetric and circulant matrices and replace them with in (10).

Without loss of generality, we assume that (M omega^{1})) is symmetric; if not, we may replace the matrixes by their symmetrized counterparts.

In fact, we think it could easily spell the future of the next-generation Matrix, or replace a car like the ho-hum econobox Toyota Echo.