Matrix Polynomial Equations, and Rational and Algebraic Matrix Equations

2007 ◽  
pp. 313-366
Keyword(s):  
Matrix Polynomial ◽  
Matrix Equations ◽  
Polynomial Equations

Matrix Polynomial Equations in Control Theory 1

1978 ◽  
Vol 11 (1) ◽  
pp. 1135-1140
Author(s):  
R. Rutman ◽  
Y. Shamash
Keyword(s):  
Control Theory ◽  
Matrix Polynomial ◽  
Polynomial Equations

scholarly journals About the solvability of matrix polynomial equations

2017 ◽  
Vol 49 (4) ◽  
pp. 670-675 ◽  
Author(s):  
Tim Netzer ◽  
Andreas Thom
Keyword(s):  
Matrix Polynomial ◽  
Polynomial Equations

scholarly journals Solving matrix polynomial equations with nested continued fractions

2021 ◽  
pp. 57-61
Author(s):  
Mykola Nedashkovskyy
Keyword(s):  
Continued Fractions ◽  
Arbitrary Order ◽  
Matrix Polynomial ◽  
Polynomial Equations

A new general approach for solving matrix polynomial equations of arbitrary order with matrix or vector unknowns is proposed in the work with the use of nested continued fractions.

scholarly journals On a class of matrix polynomial equations

2013 ◽  
Vol 439 (3) ◽  
pp. 613-620 ◽  
Author(s):  
M.A. Kaashoek ◽  
L. Lerer
Keyword(s):  
Matrix Polynomial ◽  
Polynomial Equations

Matrix equations

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Matrix Equation ◽  
Polynomial Matrix ◽  
Riccati Equations ◽  
Matrix Equations ◽  
Polynomial Equations ◽  
Linear Quadratic ◽  
Maximal Invariant ◽  
The Matrix ◽  
Quadratic Matrix ◽  
Linear Quadratic Regulators

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 chapter first considers polynomial equations, with the matrix equation Zⁿ + A n−1 Z n−1 + ... + A₁Z + A₀ = 0. It then studies quadratic matrix equations of the form ZBZ + ZA − DZ − C = 0. Finally, this chapter specializes the latter equation by introducing certain symmetries and changing the notation somewhat, until it takes on the form ZDZ + ZA + A*Z − C = 0.

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