scholarly journals Periodic matrix difference equations and companion matrices in blocks: some applications

2021 ◽  
Author(s):  
H. Benkhaldoun ◽  
R. Ben Taher ◽  
M. Rachidi
Keyword(s):  
Difference Equations ◽  
Finite Product ◽  
Periodic Matrix ◽  
Recursive Sequences ◽  
Matrix Difference Equations ◽  
Companion Matrices ◽  
Working Out

AbstractThis study is devoted to some periodic matrix difference equations, through their associated product of companion matrices in blocks. Linear recursive sequences in the algebra of square matrices in blocks and the generalized Cayley–Hamilton theorem are considered for working out some results about the powers of matrices in blocks. Two algorithms for computing the finite product of periodic companion matrices in blocks are built. Illustrative examples and applications are considered to demonstrate the effectiveness of our approach.

Ψ-stability for nonlinear matrix difference equations

2021 ◽  
Author(s):  
T. Srinivasa Rao ◽  
G. Suresh Kumar ◽  
Ch. Vasavi ◽  
T. Nageswara Rao
Keyword(s):  
Difference Equations ◽  
Nonlinear Matrix ◽  
Matrix Difference Equations

scholarly journals MODEL OF FINITE INHOMOGENEOUS CAVITY CHAIN AND APPROXIMATE METHODS OF ITS ANALYSIS

2021 ◽  
pp. 28-37
Author(s):  
M.I. Ayzatsky
Keyword(s):  
Integral Equations ◽  
Difference Equations ◽  
Decomposition Method ◽  
Wkb Approximation ◽  
Coupled Resonators ◽  
Approximate Methods ◽  
New Approach ◽  
Its Analysis ◽  
Matrix Difference Equations ◽  
Inhomogeneous Disk

A new approach to the description of an inhomogeneous chain of coupled resonators (inhomogeneous disk waveguides) is proposed. New matrix difference equations based on the technique of coupled integral equations and the decomposition method are obtained. Various approximate approaches have been developed, including the WKB approximation.

scholarly journals Iterative approximation of fixed points of generalized weak Presic type k-step iterative method for a class of operators

Filomat ◽  
2015 ◽  
Vol 29 (4) ◽  
pp. 713-724 ◽  
Author(s):  
Mujahid Abbas ◽  
Dejan Ilic ◽  
Talat Nazir
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Difference Equations ◽  
Global Attractivity ◽  
Iterative Approximation ◽  
Type K ◽  
Matrix Difference Equations

In this paper, we study the convergence of the generalized weak Presic type k-step iterative method for a class of operators f:Xk ? X satisfying Presic type contractive conditions. We also obtain the global attractivity results for a class of matrix difference equations.

scholarly journals O(N)-matrix difference equations and a nested Bethe ansatz

2012 ◽  
Vol 45 (5) ◽  
pp. 055207
Author(s):  
Hrachya M Babujian ◽  
Angela Foerster ◽  
Michael Karowski
Keyword(s):  
Bethe Ansatz ◽  
Difference Equations ◽  
Nested Bethe Ansatz ◽  
Matrix Difference Equations

scholarly journals The Stability Cone for a Difference Matrix Equation with Two Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
S. A. Ivanov ◽  
M. M. Kipnis ◽  
V. V. Malygina
Keyword(s):  
Neural Networks ◽  
Difference Equations ◽  
Matrix Equation ◽  
Geometric Algorithms ◽  
Difference Matrix ◽  
The Matrix ◽  
Two Delays ◽  
Matrix Difference Equations ◽  
The Stability

We provide geometric algorithms for checking the stability of matrix difference equations with two delays such that the matrix is nilpotent. We give examples of how our results can be applied to the study of the stability of neural networks.

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