Sentence examples for matrix equations as from inspiring English sources

Least-squares-based iterative algorithms are very important in system identification, parameter estimation, and signal processing, including the recursive least squares (RLS) and iterative least squares (ILS) methods for solving the solutions of some matrix equations, for example, the Lyapunov matrix equation, Sylvester matrix equations, and coupled matrix equations as well.

General coupled matrix equation (1) (including the generalized coupled Sylvester matrix equations as special cases) may arise in many areas of control and system theory.

∑ j = 1 q A i j X j B i j = M i, i = 1, 2, …, p. (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory.

Hajarian [19] derived a simple and efficient matrix algorithm to solve the general coupled matrix equations (sum_{j = 1}^{p} A_{ij}X_{j}B_{ij} = C_{i}), (i = 1,2, ldots,p) (including several linear matrix equations as particular cases) based on the conjugate gradients squared (CGS) method.

Dehghan and Hajarian [18] constructed an iterative method to solve the general coupled matrix equations (sum_{j = 1}^{p} A_{ij}X_{j}B_{ij} = M_{i}), (i = 1,2, ldots,p) (including the generalized (coupled) Lyapunov and Sylvester matrix equations as particular cases) over generalized bisymmetric matrix group ((X_{1},X_{2}, ldots,X_{p})) by extending the idea of conjugate gradient (CG) method.

To find the solution of this equation by NHPM, we will treat the matrix equation as a system of fractional-order differential equations (4.33).

Equation (6) can be written in the matrix equation as mathbf{Y}=mathbf{D}{mathbf{U}}^{mathrm{T}}, mathrm{with} mathbf{U}=mathbf{C}mathbf{ Z }7).

In recent years, several linear matrix equations such as Lyapunov and Sylvester matrix equations have received considerable attention due to their important applications in engineering and applied mathematics.

Strategies for team decision problems, including optimal control, N-player games (H-infinity control and non-zero sum), and so on are normally solved for off-line by solving associated matrix equations such as the coupled Riccati equations or coupled Hamilton Jacobi equations.

They arise in solving matrix equations such as the Sylvester equation.

In Section 4 we present, for the fourth order eigenvalue problems investigated in this paper, the two different characterizations of self-adjoint operators used in Section 3 as matrix equations.