zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations. (English) Zbl 1196.65081

Authors’ abstract: The generalised coupled Sylvester matrix equations

AXB+CYD=JEXF+GYH=K,

with unknown matrices X and Y, have important applications in control and system theory. Also, it is well known that reflexive and anti-reflexive matrices have wide applications in many fields. In this article, we consider the generalised coupled Sylvester matrix equations over reflexive and anti-reflexive matrices. First we propose two new matrix equations equivalent to the generalised coupled Sylvester matrix equations over reflexive and anti-reflexive matrices, respectively. Then, two new iterative algorithms are proposed for solving these matrix equations. A convergence analysis of the proposed iterative algorithms is derived. Finally, some numerical examples are presented to illustrate the theoretical results of this article.

MSC:
65F30Other matrix algorithms
15A24Matrix equations and identities
65F10Iterative methods for linear systems