Results 231 to 240 of about 2,188,246 (287)

Matrix Functions and Matrix Equations

2015
Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed.
Zhaojun Bai, Weiguo Gao, Yangfeng Su
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Matrix Riccati Differential Equations

Journal of the Society for Industrial and Applied Mathematics, 1965
Chiellini [1] considered this system, and showed that knowledge of n solutions, not on the same (n 2) -flat, reduced the solution to quadratures (this generalizes (I)). In [2] it was shown that knowledge of k suitably independent solutions, 1 < k < n, reduces the solution to k quadratures and the solution of a matrix-vector linear homogeneous system of
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Generating equations approach for quadratic matrix equations

Numerical Linear Algebra with Applications, 1999
The 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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Matrix operator equations

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, L. Ya. Savel’ev, S. V. Balakin   +2 more
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Solving Matrix Polynomial Equations

Cybernetics and Systems Analysis
Matrix 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, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knobloch, H. W., Pohl, M.
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Linear Matrix Equations

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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Appendix: Matrix Equations

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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Matrix Rotational Equations

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, Robert E. Roberson, Jens Wittenburg   +2 more
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Lagrange matrix equations

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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