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The Solutions of Matrix Equation AX=B Over a Matrix Inequality Constraint
SIAM Journal on Matrix Analysis and Applications, 2012In this paper a feasible and effective algorithm is proposed to find solutions to the matrix equation $AX=B$ subject to a matrix inequality constraint $CXD\geq E$. Numerical experiments are performed to illustrate the applicability of the algorithm.
Zhen-yun Peng, Lin Wang, Jing-jing Peng
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On Polynomial Matrix Equations
The College Mathematics Journal, 1986(1986). On Polynomial Matrix Equations. The College Mathematics Journal: Vol. 17, No. 5, pp. 388-391.
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On a Nonlinear Matrix Equation Arising in Nano Research
SIAM Journal on Matrix Analysis and Applications, 2012The matrix equation $X+A^{\top}X^{-1}A=Q$ arises in Green's function calculations in nano research, where $A$ is a real square matrix and $Q$ is a real symmetric matrix dependent on a parameter and is usually indefinite.
Chun-Hua Guo +2 more
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Lagrange matrix equations [PDF]
Russian Mathematics, 2015 In this paper, we proceed with studying matrix equations over “skew series”. We establish conditions for splitting a Lagrange matrix equation into a set of scalar differential equations. We consider diagonal, triangular, nil-triangular, and dual-diagonal forms of its solution.
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A Nontrivial Solution to a Stochastic Matrix Equation
, 2012If A is a nonsingular matrix such that its inverse is a stochastic matrix, the classic Brouwer fixed point theorem implies that the matrix equation AXA = XAX has a nontrivial solution.
Jiu Ding, N. Rhee
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HSS-like method for solving complex nonlinear Yang–Baxter matrix equation
Engineering computations, 2020M. Dehghan, Akbar Shirilord
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Matrix Equations and Transformations
1986In this chapter we consider solutions of a linear set of equations using some of the concepts discussed in Chapter 4. In addition, we introduce the concepts of a vector space, rank of a matrix, and so on. We end the chapter with a discussion of various transformations that are popular in the digital signal processing area.
John E. Hershey, R. K. Rao Yarlagadda
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On the matrix Riccati equation
IEEE Transactions on Automatic Control, 1967The matrix Riccati equation and its relation to optimization, sensitivity, and stability problems in linear systems is noted. Explicit solutions are summarized for several particular cases with emphasis on direct and unified proofs. In the stationary case, a direct proof is given for the well-known relation between solutions of the Riccati differential
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2021
The Lyapunov equation and the algebraic Riccati equation are treated in depth. The Lyapunov equation arises as the equation for the asymptotic covariance matrix of the state of a stationary Gaussian system. The algebraic Riccati equation arises in the Kalman filter, in stochastic control, and in stochastic realization of a Gaussian system.
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The Lyapunov equation and the algebraic Riccati equation are treated in depth. The Lyapunov equation arises as the equation for the asymptotic covariance matrix of the state of a stationary Gaussian system. The algebraic Riccati equation arises in the Kalman filter, in stochastic control, and in stochastic realization of a Gaussian system.
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1971
We take up here with Eq. 9 of Lecture 12, and consider the last term $$\sum\limits_{j,k} {{m^j}{{\underline d }^{ij}} \times } {\underline {\ddot b} ^{kj}}$$ .
Peter W. Likins +2 more
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We take up here with Eq. 9 of Lecture 12, and consider the last term $$\sum\limits_{j,k} {{m^j}{{\underline d }^{ij}} \times } {\underline {\ddot b} ^{kj}}$$ .
Peter W. Likins +2 more
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