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Generating equations approach for quadratic matrix equations
Numerical Linear Algebra with Applications, 1999The author gives an algorithm for the numerical solution of a quadratic matrix equation with the Hamiltonian matrix. The algorithm transforms the Hamiltonian matrix into a skew-Hamiltonian one. This is then transformed in several steps into a block diagonal matrix with the left upper block having again a block-diagonal structure with blocks of order 1 ...
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Journal of Applied and Industrial Mathematics, 2008
This article is devoted to the theory and applications of matrix operator equations in normed spaces. We describe in detail the general properties of matrix operators and their representing matrices. As the indexing set we take an arbitrary countable set.
M. M. Lavrent’ev +2 more
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This article is devoted to the theory and applications of matrix operator equations in normed spaces. We describe in detail the general properties of matrix operators and their representing matrices. As the indexing set we take an arbitrary countable set.
M. M. Lavrent’ev +2 more
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Solving Matrix Polynomial Equations
Cybernetics and Systems AnalysisMatrix equations and systems of matrix equations are widely used in problems of optimization of control systems, in mathematical economics. However, methods for solving them are developed only for the most popular matrix equations – the Riccati and Lyapunov equations, and there is no universal approach to solving problems of this class.
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On Riccati Matrix Differential Equations
Results in Mathematics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knobloch, H. W., Pohl, M.
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1995
Abstract In this chapter we present a self-contained account of some well-known facts concerning solutions of linear matrix equations. Our attention is restricted mainly to the Lyapunov and Stein equations: SA-BS=Γ, and S-BSA=Γ, respectively (see equations (5.2.3) and (5.2.4) below). In particular, their symmetric forms (when B = A*, Γ *
Peter Lancaster, Leiba Rodman
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Abstract In this chapter we present a self-contained account of some well-known facts concerning solutions of linear matrix equations. Our attention is restricted mainly to the Lyapunov and Stein equations: SA-BS=Γ, and S-BSA=Γ, respectively (see equations (5.2.3) and (5.2.4) below). In particular, their symmetric forms (when B = A*, Γ *
Peter Lancaster, Leiba Rodman
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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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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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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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Solution of Modified Matrix Equations
SIAM Journal on Numerical Analysis, 1987The purpose of this article is to present a general, computationally efficient, rank r matrix modification scheme for the solution of the linear matrix equation \(H'x'=u'\); it is assumed that the matrix H' differs by a matrix of low rank from a matrix H of a system whose solution is known, or easily computed.
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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