Results 151 to 160 of about 3,138,968 (195)

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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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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ON THE THEORY OF THE MATRIX RICCATI EQUATION

Mathematics of the USSR-Sbornik, 1992
See the review Zbl 0747.49006.
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Matrix Bernoulli equations. II

Russian Mathematics, 2008
In this paper, we find sufficient conditions for the solvability by quadratures of J. Bernoulli's equation defined over the set M2 of square matrices of order 2. We consider the cases when such equations are stated in terms of bases of a two-dimensional abelian algebra and a three- dimensional solvable Lie algebra over M2.
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On Matrix Equations of Twinning in Crystals

Mathematics and Mechanics of Solids, 2000
The algebraic equation of twinning involves a unimodular matrix, a general nonsingular matrix, a rotation, and two vectors. This paper generalizes the investigations of Ericksen, Pitteri, Zanzotto, and Gurtin by listing for each given unimodular matrix all the solutions of the twinning equation; that is, listing all the possibilities of the other ...
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Solution of Modified Matrix Equations

SIAM Journal on Numerical Analysis, 1987
The 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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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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Matrix Differential Equations

American Journal of Mathematics, 1934
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Matrix Equations

2013
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Characteristic equation of a matrix

ACM SIGPLAN Notices, 1970
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