Detail publikace

# Asymptotic Behavior of the Delayed Matrix Exponential Function

Originální název

Asymptotic Behavior of the Delayed Matrix Exponential Function

Anglický název

Asymptotic Behavior of the Delayed Matrix Exponential Function

Jazyk

en

Originální abstrakt

The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.

Anglický abstrakt

The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.

BibTex

``````
@inproceedings{BUT150437,
author="Zdeněk {Svoboda} and Josef {Diblík}",
title="Asymptotic Behavior of the Delayed Matrix Exponential Function",
annote="The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix
cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.",
address="American Institute of Physics",
booktitle="INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)",
chapter="150437",
doi="10.1063/1.5044021",
howpublished="online",
institution="American Institute of Physics",
year="2018",
month="july",
pages="430006-1--430006-4",
publisher="American Institute of Physics",
type="conference paper"
}``````