Results 161 to 170 of about 2,914,259 (200)

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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Numerical Range of Matrix Polynomials

SIAM Journal on Matrix Analysis and Applications, 1994
Let \(A_ i\), \(i = 1, \dots, m\) be \(n \times n\) matrices with complex coefficients and consider the matrix polynomial \(P(\lambda) = \sum_{i=0}^ m A_ i \lambda^ i\). The numerical range of \(P(\lambda)\) is defined through \[ W \bigl( P(\lambda) \bigr) : = \{\mu \in \mathbb{C} \mid x^* P(\mu)x = 0 \quad \text{for some nonzero} \quad x \in \mathbb{C}
Li, Chi-Kwong, Rodman, Leiba
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Orthogonal Matrix Polynomials

1990
An overview is given of some classical and recent results concerning zeros of orthogonal matrix polynomials on the unit circle. The basic questions are: How these zeros are located in the complex plane? Conversely, what conditions on the location of the zeros of a given matrix polynomial ensure that the polynomial is orthogonal?
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On solvents of matrix polynomials

Applied Numerical Mathematics, 2003
The author considers the matrix equation \(X^m+A_1X^{m-1}+\ldots +A_m=0\) where the matrices \(A_i\) and \(X\) are complex and \(n\times n\). The author reviews the basic theory of matrix polynomials and the construction of solvents of such equations in terms of the concept of eigenpair.
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Polynomial and Matrix Near-Rings

Arabian Journal for Science and Engineering, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Computing the Invariant Polynomials of a Polynomial Matrix. II

Journal of Mathematical Sciences, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stability criteria of matrix polynomials

International Journal of Control, 2019
G. Hu, Xiuling Hu
semanticscholar   +1 more source

A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error

Calcolo, 2018
M. I. Bueno, F. Dopico, S. Furtado, L. Medina   +3 more
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Matrix Polynomials

2013
Jörg Liesen, Christian Mehl
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Efficient Evaluation of Matrix Polynomials

Parallel Processing and Applied Mathematics, 2017
Niv Hoffman, O. Schwartz, Sivan Toledo
semanticscholar   +1 more source