Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)

Abstract

In this paper, we investigate the parametric generalised Sylvester matrix equation $A\left(p\right)XB\left(p\right)+C\left(p\right)XD\left(p\right)=F\left(p\right)$, 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

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Milan Hladík http://orcid.org/0000-0002-7340-8491

Additional information

Funding

M. Hladík was supported by project CE-ITI (GAP202/12/G061) of the Czech Science Foundation (Grantová Agentura České Republiky).

Notes on contributors

Marzieh Dehghani-Madiseh

Marzieh Dehghani-Madiseh is an assistant professor of mathematics at Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran. In 2015, she spent her sabbatical stay at Department of Applied Mathematics, Charles University in Prague. Her research interests include the areas of numerical analysis, numerical linear algebra and interval computations.

Milan Hladík

Milan Hladík obtained his PhD in “Econometrics and operations research” from the Faculty of Mathematics and Physics, Charles University in Prague. In 2008, he worked as a postdoc researcher in Coprin team at INRIA, Sophia Antipolis, France. Now, he is an associate professor at the Department of Applied Mathematics of the Charles University in Prague. He published more than 60 original research journal papers in interval computation, numerical analysis, optimization and operations research. He is a member of the editorial board of European Journal of Operational Research, Reliable Computing and International Journal of Fuzzy Computation and Modelling.