Dynamical System Modeling and Stability Investigation�DSMSI-2023

Dedicated to the 77th anniversary of the outstanding Ukrainian scientist

professor Denys Khusainov

December 19-21, 2023, Kyiv, Ukraine

Algorithm for finding a positive definite solution to the Sylvester matrix equation

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Oleksii Bychkov^a, Ganna Marzafey ^a and George Dimitrov ^b

Taras Shevcenko National University of Kyjv, Volodymyrska str. 60, Kyjv, Ukraine, 01601

^bUniversity of Library Studies and Information Technologies, Blvd. “Tsarigradsko Shose” 119, 7-Kilometar, Sofia, Bulgaria, 1784

Introduction

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Introduction

• It is noted that there are now several approaches to solving the Sylvester equation. The first is to reduce the matrix equation to a vector (linear algebraic equation of increased dimension) and then the condition for the solvability of this equation is expressed through the non-degeneracy of the corresponding matrix. The second approach uses the small parameter method. It is also possible to obtain a spectral sparsity criterion for an equation with mutually commutable matrices. An analytical solution of this equation is possible only for the case of the two-term Sylvester equation.

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Main result

Dynamical System Modeling and Stability Investigation, DSMSI-2023

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