Results 261 to 270 of about 419,229 (311)

On the matrix riccati equation

Information Sciences, 1971
Properties of the algebraic equation A^TX+XA-XBQ"2^-^1B^TX+Q"1=0 are studied for arbitrary nonnegative definite and positive definite matrices Q"1 and Q"2. The results are used to study the possible number of stationary solutions of the Riccati equation.
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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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Fuzzy linear matrix equation

Fuzzy Optimization and Decision Making, 2009
The authors analyze fuzzy linear matrix equations of the form \(AXB=C\) for finding its fuzzy solutions, using the parametric form of the fuzzy linear system. The authors also derive necessary and sufficient conditions for the existence of the set of fuzzy solutions.
Tofigh Allahviranloo, Nasser Mikaeilvand, M. Barkhordary   +2 more
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Matrix equations

2014
This chapter presents applications to polynomial matrix equations, algebraic Riccati equations, and linear quadratic regulators. Without attempting to develop in-depth exposition of the topics, this chapter details these applications in basic forms. Here, maximal invariant semidefinite or neutral subspaces will play a key role. The
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On the matrix equation

Linear and Multilinear Algebra, 2017
AbstractIn this paper we investigate the matrix equation . Some sufficient and necessary conditions for the existence of Hermitian positive definite solutions as well as for the existence of the smallest Hermitian positive definite solution of the considered equation are derived.
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On the Discrete Riccati Matrix Equation

SIAM Journal on Algebraic Discrete Methods, 1985
This paper gives a lower bound for the determinant of the positive definite solution of the discrete algebraic Riccati matrix equation. The authors state in the introduction that many iterative methods to solve the Riccati equation require an initial guess of the solution and that the lower bound they give may be useful for estimating the ''size'' of ...
Minh Thanh Tran, Sawan, Mahmoud E.
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Differential Equation for the Transfer Matrix

International Journal of Theoretical Physics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shelykh, I. A., Ivanov, V. K.
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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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Comments on "On the Lyapunov matrix equation"

IEEE Transactions on Automatic Control, 1975
The Lyapunov matrix equation A'Q + QA = - P is considered in the above paper, where two fundamental inequalities are derived which are satisfied by the extremal eigenvalues of the matrices Q and P provided A is a stability matrix. Similar results are derived by an alternate more simple and straightforward approach using matrix norms.
Montemayor, J. J., Womack, Baxter F.
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On a quadratic matrix equation associated with an M-matrix

IMA Journal of Numerical Analysis, 2003
The main purpose of this work is to study the quadratic matrix equation \( X^{2}-EX-F=0\) where \(E,F,X\in \mathbb{R}^{n\times n}\), \(E\) is diagonal and \(F\) is an \( M\)-matrix. The main approach that the authors are using for solving the above quadratic matrix equation, is by transforming it into an equation that belongs to a special class of non ...
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