Marzieh Dehghani-Madiseh and Milan Hladík. Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p). Int. J. Syst. Sci., 50(11):2153–2167, 2019.
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In this paper, we investigate the parametric generalised Sylvester matrix equation A(p)XB(p)+C(p)XD(p)=F(p), whose elements are linear functions of uncertain parameters varying within intervals. This model generalises both interval matrix equations and parametric interval linear systems, so it is a quite general model. First, we give some sufficient conditions under which the solution set of this parametric equation is bounded. We then propose several approaches for enclosing the solution set that acquire tighter enclosures than those obtained by relaxing the parametric system to an interval system. Some special cases of interval systems that inherently are parametric (have dependent structure) are considered, too. Finally, numerical experiments are given to illustrate the effectiveness of the proposed methods.
@article{DehHla2019a,
author = "Dehghani-Madiseh, Marzieh and Milan Hlad\'{\i}k",
title = "Enclosing the solution set of the parametric generalised Sylvester matrix equation {$A(p)XB(p) + C(p)XD(p) = F(p)$}",
webtitle = "Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)",
journal = "Int. J. Syst. Sci.",
fjournal = "International Journal of Systems Science",
volume = "50",
number = "11",
pages = "2153-2167",
year = "2019",
doi = "10.1080/00207721.2019.1647306",
issn = "0020-7721",
issnonline = "1464-5319",
url = "https://www.tandfonline.com/doi/full/10.1080/00207721.2019.1647306",
bib2html_dl_html = "https://www.tandfonline.com/eprint/RBQD74FX3TRUWFSD5JVY/full?target=10.1080/00207721.2019.1647306",
bib2html_dl_pdf = "https://doi.org/10.1080/00207721.2019.1647306",
abstract = "In this paper, we investigate the parametric generalised Sylvester matrix equation A(p)XB(p)+C(p)XD(p)=F(p), whose elements are linear functions of uncertain parameters varying within intervals. This model generalises both interval matrix equations and parametric interval linear systems, so it is a quite general model. First, we give some sufficient conditions under which the solution set of this parametric equation is bounded. We then propose several approaches for enclosing the solution set that acquire tighter enclosures than those obtained by relaxing the parametric system to an interval system. Some special cases of interval systems that inherently are parametric (have dependent structure) are considered, too. Finally, numerical experiments are given to illustrate the effectiveness of the proposed methods.",
keywords = "Interval computation; Interval linear systems; Parameterised systems; Generalised Sylvester matrix equations",
}
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