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About 10,000 papers for “Matrix polynomial”

On Polynomial Matrix Equations

Harley Flanders · College Mathematics Journal · 1986

(1986). On Polynomial Matrix Equations. The College Mathematics Journal: Vol. 17, No. 5, pp. 388-391.

Cited by 1

Solving matrix polynomial equations

M. Nedashkovskyy · Kibernetyka ta Systemnyi Analiz · 2025

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. This paper discusses methods for solving matrix polynomial equations of arbitrary order with matrix and vector unknowns. An approach to calculating tuples of solutions of polynomial matrix equations, which is based on the theory of branched chain fractions, is given. It should be noted that we are talking not only about numerical but also symbolic methods of solution. The paper also presents a computational scheme for systems of second-degree polynomial matrix equations with many unknowns. The solution is developed into a continued matrix fraction. Sufficient signs of convergence of branched continued matrix fractions to the solutions and the criteria for completing calculations in iterative procedures are formulated. The results of numerical experiments are presented, confirming the validity of the theoretical calculations and the effectiveness of the proposed methods. Keywords: matrix polynomial equations, branched continued fractions with matrix elements, convergence to solution.

Cited by 0Open access

Inverse polynomial matrix approximation

Kisielewicz, Jerzy W. · Digital library of Zielona Gora (University of Zielona Góra) · 1993

A computational algorithm for matrix C(z) which approximates the inverse of a given matrix Y(z) is described in this paper.

Cited by 0Open access

Systolic architectures for polynomial and polynomial matrix manipulations

T. Faber, Stanisław H. Żak · International Journal of Systems Science · 1987

Manipulations of polynomials and polynomial matrices, basic to the polynomial equation approach to control system design, are dissected in a manner suitable for repeatable, rhythmic solution. These solutions are then implemented on systolic arrays. An introduction to a systematic design and analysis procedure for systolic arrays, along with an example, concludes the paper.

Cited by 0

Polynomial Detection of Matrix Subalgebras

Daniel Birmajer · ArXiv.org · 2004

It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree $4n$ is a polynomial identity for the algebra of n by n matrices over a field F. Using a strengthened version of this result obtained by Domokos, we show that the double Capelli polynomial of total degree 4n-2 is a polynomial identity for any proper matrix subalgebra. Subsequently, we present a similar result for nonsplit extensions of full matrix algebras.

Cited by 0Open access

Evaluation of a matrix polynomial

A. Fath · IEEE Transactions on Automatic Control · 1968

A simple method is proposed to reduce the computational requirements for evaluation of matrix polynomials. An example is given indicating its use in evaluating e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sup> arising in the solution of linear differential equations.

Cited by 7

Polynomial matrix algebra with applications

Weiss, Stephan, Proudler, Ian K., Coutts, Fraser K. · Strathprints: The University of Strathclyde institutional repository (University of Strathclyde) · 2023

[Abstract unavailable]

Cited by 0Open access