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)
An iterative algorithm for the least squares generalized reflexive solutions of the matrix equations AXB=E, CXD=F. (English) Zbl 1242.65085
Summary: The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: ||(AXB CXD)-(E F)||=min over a generalized reflexive matrix X. For any initial generalized reflexive matrix X 1 , by the iterative algorithm, the generalized reflexive solution X * can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution X * can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution X ^ to a given matrix X 0 in Frobenius norm can be derived by finding the least-norm generalized reflexive solution X ˜ * of a new corresponding minimum Frobenius norm residual problem: min||(AX ˜B CX ˜D)-(E ˜ F ˜) with E ˜=E-AX 0 B,F ˜=F-CX 0 D. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.
MSC:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
15A24Matrix equations and identities