Results 261 to 270 of about 172,193 (304)

Matrix Riccati equations and systems structure

1973 IEEE Conference on Decision and Control including the 12th Symposium on Adaptive Processes, 1973
A new algorithm for solving discrete time linear-quadratic control problems is given. This algorithm is shown to be a special case of the "structure algorithm" used for characterizing properties of linear systems. It is also shown to be related to the Chandrasekhar-type equations recently introduced by Kailath.
H. Payne, L. Silverman
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A system of equations with a tridiagonal coefficient matrix

Applied Mathematics and Computation, 2004
The goal of the paper is to show that for a linear system of equations \(AX=C\), where the coefficient matrix \(A\) is tridiagonal, the algorithms used by \textit{M. El-Mikkawy} in [Appl. Math. Comput. 139, No. 2--3, 503--511 (2003; Zbl 1078.65533)] can be improved in the case when \(A\) is invertible, the system being equivalent with a linear system ...
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A Note on Kronecker Matrix Products and Matrix Equation Systems

SIAM Journal on Applied Mathematics, 1969
where B' is the transpose of B. It has been shown that Definition 1 and Theorem 1 can fruitfully be applied to problems of matrix differentiation [2]. In this note it will be shown that they can be applied to a more general class of linear matrix equations, including linear matrix differential equations.
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A system of matrix equations and its applications

Science China Mathematics, 2013
For the following system of matrix equations, \(A_1X = {C_1}\), \({A_2}Y = {C_2}\), \(Y{B_2} = {D_2}\), \(Y = {Y^ * }\), \({A_3}Z = {C_3}\), \(Z{B_3} = {D_3}\), \(Z = {Z^ * }\), \({B_4}X + {({B_4}X)^ * } + {C_4}YC_4^ * + {D_4}ZD_4^ * = {A_4}\), solvability conditions are proved, a general solution is formulated, and the maximal and minimal ranks and ...
Wang, QingWen, He, ZhuoHeng
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Reflexive solution to a system of matrix equations

Journal of Shanghai University (English Edition), 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chang, Haixia, Wang, Qingwen
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Solution of the Lyapunov matrix equation for a system with a time‐dependent stiffness matrix

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2003
AbstractThe stability of the linearized model of a rotor system with non‐symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces.
Pommer, Christian, Kliem, Wolfhard
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Lyapunov's matrix equation with system matrix in companion form

International Journal of Control, 1993
Abstract A simple method for solving Lyapunov's matrix equation for linear continuous systems with the system matrix in companion form is proposed. The method involves the inversion of the Hurwitz matrix. A necessary and sufficient condition for the existence of a solution to the equation is also obtained.
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Iterative methods for solving linear matrix equation and linear matrix system

International Journal of Computer Mathematics, 2010
In this paper, an efficient iterative method is presented to solve the linear matrix equation [image omitted] (X) = E with real matrix X. By this iterative method, the solvability of the linear matrix equation can be determined automatically. When the matrix equation is consistent, then, for any initial matrix X0, a solution can be obtained within ...
Youfeng Su, Guoliang Chen 0002
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$$\eta $$-Hermitian Solution to a System of Quaternion Matrix Equations

Bulletin of the Malaysian Mathematical Sciences Society, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xin, He, Zhuo-Heng
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Solvability of systems of linear matrix equations subject to a matrix inequality

Linear and Multilinear Algebra, 2016
In this paper, the solvability conditions and the explicit expressions of the Hermitian solutions to the system of matrix equationsand the Hermitian nonnegative definite solutions to the system of matrix equationsare, respectively, put forward, by making full use of the generalized inverse and the rank of matrices.
Juan Yu, Shu-qian Shen
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