Sentence examples for matrix equations such from inspiring English sources
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.
Another important application is the integration of matrix nonlinear evolution equations such as matrix KdV and Boomeron equations [8].
Any number of such matrix equations can always be rewritten as a system of equations whose most general form reads where P has 6 columns and 6 n rows, where n is the number of symmetry elements other than the identity involved in the special position [indeed equation (10), being trivial for, can safely be discarded].
Recently in [1], Kiliçman and Al Zhour presented the iterative solution of such coupled matrix equations based on the Kronecker convolution structures.
Further the technique has been successfully applied in various fields of matrix algebra such as, in matrix equations, matrix differential equations, matrix inequalities, and many other subjects; for details see [1, 7, 8].
Several techniques have been developed for the analysis of Petri nets, such as reachability trees, matrix equations and reachability graphs.
Nowadays, matrix equations are very useful in numerous applications such as control theory [1, 2], vibration theory [3], image processing [4, 5] and so on.
Many problems in various areas, such as differential equations, integral equations, boundary value problems and nonlinear matrix equations, can be converted to the operator equation (1.1).
Computer-simulation examples substantiate the efficacy of such a ZNN model in the context of solution of time-varying generalized linear matrix equations.
